diff --git a/Library/Homebrew/dev-cmd/bump.rb b/Library/Homebrew/dev-cmd/bump.rb
index 75456b853e..4e19251dde 100644
--- a/Library/Homebrew/dev-cmd/bump.rb
+++ b/Library/Homebrew/dev-cmd/bump.rb
@@ -25,12 +25,15 @@ module Homebrew
              description: "Check only formulae."
       switch "--cask", "--casks",
              description: "Check only casks."
+      switch "--open-pr",
+             description: "Open a pull request for the new version if there are none already open."
       flag   "--limit=",
              description: "Limit number of package results returned."
       flag   "--start-with=",
              description: "Letter or word that the list of package results should alphabetically follow."
 
       conflicts "--cask", "--formula"
+      conflicts "--no-pull-requests", "--open-pr"
 
       named_args [:formula, :cask]
     end
@@ -103,7 +106,7 @@ module Homebrew
         end
 
         package_data = Repology.single_package_query(name, repository: repository)
-        retrieve_and_display_info(
+        retrieve_and_display_info_and_open_pr(
           formula_or_cask,
           name,
           package_data&.values&.first,
@@ -157,7 +160,13 @@ module Homebrew
           end
 
           puts if i.positive?
-          retrieve_and_display_info(formula_or_cask, name, repositories, args: args, ambiguous_cask: ambiguous_cask)
+          retrieve_and_display_info_and_open_pr(
+            formula_or_cask,
+            name,
+            repositories,
+            args:           args,
+            ambiguous_cask: ambiguous_cask,
+          )
         end
       end
     end
@@ -205,44 +214,59 @@ module Homebrew
       pull_requests = pull_requests.map { |pr| "#{pr["title"]} (#{Formatter.url(pr["html_url"])})" }.join(", ")
     end
 
-    return "none" if pull_requests.blank?
-
     pull_requests
   end
 
-  def retrieve_and_display_info(formula_or_cask, name, repositories, args:, ambiguous_cask: false)
-    current_version = if formula_or_cask.is_a?(Formula)
-      formula_or_cask.stable.version
+  def retrieve_and_display_info_and_open_pr(formula_or_cask, name, repositories, args:, ambiguous_cask: false)
+    if formula_or_cask.is_a?(Formula)
+      current_version = formula_or_cask.stable.version
+      type = :formula
+      version_name = "formula version"
     else
-      Version.new(formula_or_cask.version)
+      current_version = Version.new(formula_or_cask.version)
+      type = :cask
+      version_name = "cask version   "
     end
 
+    livecheck_latest = livecheck_result(formula_or_cask)
+
     repology_latest = if repositories.present?
       Repology.latest_version(repositories)
     else
       "not found"
     end
 
-    livecheck_latest = livecheck_result(formula_or_cask)
-    pull_requests = if !args.no_pull_requests? && (args.named.present? ||
-                       (livecheck_latest.is_a?(Version) && livecheck_latest != current_version))
-      retrieve_pull_requests(formula_or_cask, name)
-    end
+    new_version = if livecheck_latest.is_a?(Version) && livecheck_latest > current_version
+      livecheck_latest
+    elsif repology_latest.is_a?(Version) && repology_latest > current_version
+      repology_latest
+    end.presence
 
-    name += " (cask)" if ambiguous_cask
+    pull_requests = if !args.no_pull_requests? && (args.named.present? || new_version)
+      retrieve_pull_requests(formula_or_cask, name)
+    end.presence
+
+    title_name = ambiguous_cask ? "#{name} (cask)" : name
     title = if current_version == repology_latest &&
                current_version == livecheck_latest
-      "#{name} #{Tty.green}is up to date!#{Tty.reset}"
+      "#{title_name} #{Tty.green}is up to date!#{Tty.reset}"
     else
-      name
+      title_name
     end
 
     ohai title
     puts <<~EOS
-      Current #{formula_or_cask.is_a?(Formula) ? "formula version:" : "cask version:   "}  #{current_version}
+      Current #{version_name}:  #{current_version}
       Latest livecheck version: #{livecheck_latest}
       Latest Repology version:  #{repology_latest}
+      Open pull requests:       #{pull_requests || "none"}
     EOS
-    puts "Open pull requests:       #{pull_requests}" unless pull_requests.nil?
+
+    return unless args.open_pr?
+    return unless new_version
+    return if pull_requests
+
+    system HOMEBREW_BREW_FILE, "bump-#{type}-pr", "--no-browse",
+           "--message=Created by `brew bump`", "--version=#{new_version}", name
   end
 end
diff --git a/Library/Homebrew/utils/repology.rb b/Library/Homebrew/utils/repology.rb
index f6ed17f485..9f64613e0a 100644
--- a/Library/Homebrew/utils/repology.rb
+++ b/Library/Homebrew/utils/repology.rb
@@ -99,6 +99,6 @@ module Repology
     # scheme
     return "no latest version" if latest_version.blank?
 
-    latest_version["version"]
+    Version.new(latest_version["version"])
   end
 end
diff --git a/completions/bash/brew b/completions/bash/brew
index 8f96bf7df3..828aac54fb 100644
--- a/completions/bash/brew
+++ b/completions/bash/brew
@@ -436,6 +436,7 @@ _brew_bump() {
       --help
       --limit
       --no-pull-requests
+      --open-pr
       --quiet
       --start-with
       --verbose
diff --git a/completions/fish/brew.fish b/completions/fish/brew.fish
index a9c3bb0af3..4a30c628e0 100644
--- a/completions/fish/brew.fish
+++ b/completions/fish/brew.fish
@@ -388,6 +388,7 @@ __fish_brew_complete_arg 'bump' -l full-name -d 'Print formulae/casks with fully
 __fish_brew_complete_arg 'bump' -l help -d 'Show this message'
 __fish_brew_complete_arg 'bump' -l limit -d 'Limit number of package results returned'
 __fish_brew_complete_arg 'bump' -l no-pull-requests -d 'Do not retrieve pull requests from GitHub'
+__fish_brew_complete_arg 'bump' -l open-pr -d 'Open a pull request for the new version if there are none already open'
 __fish_brew_complete_arg 'bump' -l quiet -d 'Make some output more quiet'
 __fish_brew_complete_arg 'bump' -l start-with -d 'Letter or word that the list of package results should alphabetically follow'
 __fish_brew_complete_arg 'bump' -l verbose -d 'Make some output more verbose'
diff --git a/completions/zsh/_brew b/completions/zsh/_brew
index d24700a36a..f7525e4080 100644
--- a/completions/zsh/_brew
+++ b/completions/zsh/_brew
@@ -478,6 +478,7 @@ _brew_bump() {
     '--help[Show this message]' \
     '--limit[Limit number of package results returned]' \
     '--no-pull-requests[Do not retrieve pull requests from GitHub]' \
+    '--open-pr[Open a pull request for the new version if there are none already open]' \
     '--quiet[Make some output more quiet]' \
     '--start-with[Letter or word that the list of package results should alphabetically follow]' \
     '--verbose[Make some output more verbose]' \
diff --git a/docs/Manpage.md b/docs/Manpage.md
index 61118b1500..3bec08d72e 100644
--- a/docs/Manpage.md
+++ b/docs/Manpage.md
@@ -926,6 +926,8 @@ formulae, also displays whether a pull request has been opened with the URL.
   Check only formulae.
 * `--cask`:
   Check only casks.
+* `--open-pr`:
+  Open a pull request for the new version if there are none already open.
 * `--limit`:
   Limit number of package results returned.
 * `--start-with`:
diff --git a/manpages/brew.1 b/manpages/brew.1
index bfb54dfe0f..34da2875fc 100644
--- a/manpages/brew.1
+++ b/manpages/brew.1
@@ -1295,6 +1295,10 @@ Check only formulae\.
 Check only casks\.
 .
 .TP
+\fB\-\-open\-pr\fR
+Open a pull request for the new version if there are none already open\.
+.
+.TP
 \fB\-\-limit\fR
 Limit number of package results returned\.
 .