diff --git a/Library/Homebrew/os/linux/elf.rb b/Library/Homebrew/os/linux/elf.rb
index efd855db952ca3..2244ffe503b61b 100644
--- a/Library/Homebrew/os/linux/elf.rb
+++ b/Library/Homebrew/os/linux/elf.rb
@@ -1,6 +1,8 @@
 # typed: true
 # frozen_string_literal: true
 
+require "os/linux/ld"
+
 # {Pathname} extension for dealing with ELF files.
 # @see https://en.wikipedia.org/wiki/Executable_and_Linkable_Format#File_header
 #
@@ -130,19 +132,7 @@ def initialize(path)
       @dylib_id, needed = needed_libraries path
       return if needed.empty?
 
-      ldd = DevelopmentTools.locate "ldd"
-      ldd_output = Utils.popen_read(ldd, path.expand_path.to_s).split("\n")
-      return unless $CHILD_STATUS.success?
-
-      ldd_paths = ldd_output.filter_map do |line|
-        match = line.match(/\t.+ => (.+) \(.+\)|\t(.+) => not found/)
-        next unless match
-
-        match.captures.compact.first
-      end
-      @dylibs = ldd_paths.select do |ldd_path|
-        needed.include? File.basename(ldd_path)
-      end
+      @dylibs = needed.map { |lib| find_full_lib_path(lib).to_s }
     end
 
     private
@@ -157,6 +147,63 @@ def needed_libraries_using_patchelf_rb(path)
       patcher = path.patchelf_patcher
       [patcher.soname, patcher.needed]
     end
+
+    def dt_flags_1(path)
+      readelf = DevelopmentTools.locate "readelf"
+      readelf_output = Utils.popen_read(readelf, "--dynamic", path.expand_path.to_s)
+      return [] unless $CHILD_STATUS.success?
+
+      match = readelf_output.match(/^\s*0x0*6ffffffb\s+\(FLAGS_1\)\s+Flags:\s*(.*)$/)
+      return [] unless match
+
+      match.captures.compact.first.split(/\s+/)
+    end
+
+    def find_full_lib_path(basename)
+      local_paths = (path.patchelf_patcher.runpath || path.patchelf_patcher.rpath)&.split(":")
+
+      # Search for dependencies in the runpath/rpath first
+      local_paths&.each do |local_path|
+        candidate = Pathname(local_path)/basename
+        return candidate if candidate.exist? && candidate.elf?
+      end
+
+      # Check if DF_1_NODEFLIB is set
+      nodeflib_flag = dt_flags_1(path).include?("NODEFLIB")
+
+      linker_library_paths = OS::Linux::Ld::library_paths
+      linker_system_dirs = OS::Linux::Ld::system_dirs
+
+      # If DF_1_NODEFLIB is set, exclude any library paths that are subdirectories
+      # of the system dirs
+      if nodeflib_flag
+        linker_library_paths = linker_library_paths.reject do |linker_library_path|
+          child = Pathname(linker_library_path).realdirpath
+
+          linker_system_dirs.any? do |linker_system_dir|
+            parent = Pathname(linker_system_dir).realdirpath
+            child.ascend { |p| break true if p == parent } || false
+          end
+        end
+      end
+
+      # If not found, search recursively in the paths listed in ld.so.conf (skipping
+      # paths that are subdirectories of the system dirs if DF_1_NODEFLIB is set)
+      linker_library_paths.each do |linker_library_path|
+        candidate = Pathname(linker_library_path)/basename
+        return candidate if candidate.exist? && candidate.elf?
+      end
+
+      # If not found, search in the system dirs, unless DF_1_NODEFLIB is set
+      unless nodeflib_flag
+        linker_system_dirs.each do |linker_system_dir|
+          candidate = Pathname(linker_system_dir)/basename
+          return candidate if candidate.exist? && candidate.elf?
+        end
+      end
+
+      basename
+    end
   end
   private_constant :Metadata
 
diff --git a/Library/Homebrew/os/linux/ld.rb b/Library/Homebrew/os/linux/ld.rb
new file mode 100644
index 00000000000000..532f7870b6acff
--- /dev/null
+++ b/Library/Homebrew/os/linux/ld.rb
@@ -0,0 +1,75 @@
+# typed: true
+# frozen_string_literal: true
+
+module OS
+    module Linux
+      # Helper functions for querying `ld` information.
+      #
+      # @api private
+      module Ld
+        module_function
+  
+        sig { returns(String) }
+        def sysconfdir
+          fallback_sysconfdir = "/etc"
+          
+          brewed_ld_so = HOMEBREW_PREFIX/"lib/ld.so"
+          return fallback_sysconfdir unless brewed_ld_so.exist?
+        
+          ld_so_output = Utils.popen_read(brewed_ld_so, "--list-diagnostics")
+          return fallback_sysconfdir unless $CHILD_STATUS.success?
+  
+          match = ld_so_output.match(/path.sysconfdir="(.+)"/)
+          return fallback_sysconfdir unless match
+          
+          match.captures.compact.first
+        end
+  
+        sig { returns(T::Array[String]) }
+        def system_dirs
+          system_dirs = []
+  
+          brewed_ld_so = HOMEBREW_PREFIX/"lib/ld.so"
+          return system_dirs unless brewed_ld_so.exist?
+        
+          ld_so_output = Utils.popen_read(brewed_ld_so, "--list-diagnostics").split("\n")
+          return system_dirs unless $CHILD_STATUS.success?
+  
+          ld_so_output.each do |line|
+            match = line.match(/path.system_dirs\[0x.*\]="(.*)"/)
+            next unless match
+            system_dirs << match.captures.compact.first
+          end
+  
+          system_dirs
+        end
+  
+        def library_paths(conf_path = Pathname(sysconfdir)/"ld.so.conf")
+          conf_file = Pathname(conf_path)
+          paths = Set.new
+          directory = conf_file.realpath.dirname
+    
+          conf_file.readlines.each do |line|
+            # Remove comments and leading/trailing whitespace
+            line.strip!
+            line.sub!(/\s*#.*$/, "")
+    
+            if line.start_with?(/\s*include\s+/)
+              include_path = Pathname(line.sub(/^\s*include\s+/, "")).expand_path
+              wildcard = include_path.absolute? ? include_path : directory/include_path
+    
+              Dir.glob(wildcard.to_s).each do |include_file|
+                paths += library_paths(include_file)
+              end
+            elsif line.empty?
+              next
+            else
+              paths << line
+            end
+          end
+    
+          paths.to_a
+        end
+      end
+    end
+  end