diff --git a/news/14193.bugfix.rst b/news/14193.bugfix.rst
new file mode 100644
index 0000000000..e9b7877ddf
--- /dev/null
+++ b/news/14193.bugfix.rst
@@ -0,0 +1,2 @@
+Fix the "no matching distributions" hint being shown for packages that are
+excluded due to version conflicts.
diff --git a/src/pip/_internal/resolution/resolvelib/factory.py b/src/pip/_internal/resolution/resolvelib/factory.py
index ff1dab54c3..4592fd0959 100644
--- a/src/pip/_internal/resolution/resolvelib/factory.py
+++ b/src/pip/_internal/resolution/resolvelib/factory.py
@@ -784,16 +784,7 @@ def _has_any_candidates(self, project_name: str) -> bool:
         """
         Check if there are any candidates available for the project name.
         """
-        return any(
-            self.find_candidates(
-                project_name,
-                requirements={project_name: []},
-                incompatibilities={},
-                constraint=Constraint.empty(),
-                prefers_installed=True,
-                is_satisfied_by=lambda r, c: True,
-            )
-        )
+        return bool(self._finder.find_all_candidates(project_name))
 
     def get_installation_error(
         self,
diff --git a/tests/functional/test_new_resolver_errors.py b/tests/functional/test_new_resolver_errors.py
index 4e204a3864..a0d76d907a 100644
--- a/tests/functional/test_new_resolver_errors.py
+++ b/tests/functional/test_new_resolver_errors.py
@@ -193,3 +193,32 @@ def test_new_resolver_no_versions_available_hint(script: PipTestEnvironment) ->
         "matching distributions available for your environment:\n"
         "    incompatible-dep\n" in result.stdout
     ), str(result)
+
+
+def test_new_resolver_hint_not_shown_when_versions_available(
+    script: PipTestEnvironment,
+) -> None:
+    """
+    Test hint is not shown when a package candidate is available,
+    even though ResolutionImpossible occurs.
+    """
+    create_basic_wheel_for_package(script, "base", "1.0")
+    create_basic_wheel_for_package(script, "base", "2.0")
+    create_basic_wheel_for_package(script, "pkga", "1.0", depends=["base==1.0"])
+    create_basic_wheel_for_package(script, "pkgb", "1.0", depends=["base==2.0"])
+
+    result = script.pip(
+        "install",
+        "--no-cache-dir",
+        "--no-index",
+        "--find-links",
+        script.scratch_path,
+        "pkga",
+        "pkgb",
+        expect_error=True,
+    )
+
+    assert "ResolutionImpossible" in result.stderr, str(result)
+    assert "pkga 1.0 depends on base==1.0" in result.stdout, str(result)
+    assert "pkgb 1.0 depends on base==2.0" in result.stdout, str(result)
+    assert "have no matching distributions available" not in result.stdout, str(result)