diff --git a/types/options.go b/types/options.go
index 7189a8e6a4..20bf5057f9 100644
--- a/types/options.go
+++ b/types/options.go
@@ -305,7 +305,11 @@ func getRootlessStorageOpts(rootlessUID int, systemOpts StoreOptions) (StoreOpti
 	}
 	if opts.GraphDriverName == "" {
 		if len(systemOpts.GraphDriverPriority) == 0 {
-			opts.GraphDriverName = "vfs"
+			if canUseRootlessOverlay(opts.GraphRoot, opts.RunRoot) {
+				opts.GraphDriverName = overlayDriver
+			} else {
+				opts.GraphDriverName = "vfs"
+			}
 		} else {
 			opts.GraphDriverPriority = systemOpts.GraphDriverPriority
 		}
diff --git a/types/options_darwin.go b/types/options_darwin.go
index eed1a3d94b..3c8ff4e4e8 100644
--- a/types/options_darwin.go
+++ b/types/options_darwin.go
@@ -11,3 +11,8 @@ const (
 var (
 	defaultOverrideConfigFile = "/etc/containers/storage.conf"
 )
+
+// canUseRootlessOverlay returns true if the overlay driver can be used for rootless containers
+func canUseRootlessOverlay(home, runhome string) bool {
+	return false
+}
diff --git a/types/options_freebsd.go b/types/options_freebsd.go
index afb7ec6b4a..be2bc2f27d 100644
--- a/types/options_freebsd.go
+++ b/types/options_freebsd.go
@@ -12,3 +12,8 @@ const (
 var (
 	defaultOverrideConfigFile = "/usr/local/etc/containers/storage.conf"
 )
+
+// canUseRootlessOverlay returns true if the overlay driver can be used for rootless containers
+func canUseRootlessOverlay(home, runhome string) bool {
+	return false
+}
diff --git a/types/options_linux.go b/types/options_linux.go
index d44aaf76a3..a28e82883c 100644
--- a/types/options_linux.go
+++ b/types/options_linux.go
@@ -1,5 +1,13 @@
 package types
 
+import (
+	"os/exec"
+	"strconv"
+	"strings"
+
+	"golang.org/x/sys/unix"
+)
+
 const (
 	// these are default path for run and graph root for rootful users
 	// for rootless path is constructed via getRootlessStorageOpts
@@ -12,3 +20,33 @@ const (
 var (
 	defaultOverrideConfigFile = "/etc/containers/storage.conf"
 )
+
+// canUseRootlessOverlay returns true if the overlay driver can be used for rootless containers
+func canUseRootlessOverlay(home, runhome string) bool {
+	// we check first for fuse-overlayfs since it is cheaper.
+	if path, _ := exec.LookPath("fuse-overlayfs"); path != "" {
+		return true
+	}
+
+	// We cannot use overlay.SupportsNativeOverlay since canUseRootlessOverlay is called by Podman
+	// before we enter the user namespace and the driver we pick here is written in the podman database.
+	// Checking the kernel version is usually not a good idea since the feature could be back-ported, e.g. RHEL
+	// but this is just an heuristic and on RHEL we always install the storage.conf file.
+	// native overlay for rootless was added upstream in 5.13 (at least the first version that we support), so check
+	// that the kernel is >= 5.13.
+	var uts unix.Utsname
+	if err := unix.Uname(&uts); err == nil {
+		parts := strings.Split(string(uts.Release[:]), ".")
+		major, _ := strconv.Atoi(parts[0])
+		if major >= 6 {
+			return true
+		}
+		if major == 5 && len(parts) > 1 {
+			minor, _ := strconv.Atoi(parts[1])
+			if minor >= 13 {
+				return true
+			}
+		}
+	}
+	return false
+}
diff --git a/types/options_test.go b/types/options_test.go
index 53ca9f9179..23bc6d2868 100644
--- a/types/options_test.go
+++ b/types/options_test.go
@@ -19,6 +19,27 @@ func TestGetRootlessStorageOpts(t *testing.T) {
 
 	const vfsDriver = "vfs"
 
+	t.Run("systemDriver=<unset>", func(t *testing.T) {
+		systemOpts := StoreOptions{}
+
+		td := t.TempDir()
+		home := filepath.Join(td, "unset-driver-home")
+		runhome := filepath.Join(td, "unset-driver-runhome")
+		defer os.RemoveAll(home)
+		defer os.RemoveAll(runhome)
+
+		systemOpts.GraphRoot = home
+		systemOpts.RunRoot = runhome
+		storageOpts, err := getRootlessStorageOpts(os.Geteuid(), systemOpts)
+
+		assert.NilError(t, err)
+		expectedDriver := vfsDriver
+		if canUseRootlessOverlay(home, runhome) {
+			expectedDriver = overlayDriver
+		}
+		assert.Equal(t, storageOpts.GraphDriverName, expectedDriver)
+	})
+
 	t.Run("systemDriver=btrfs", func(t *testing.T) {
 		systemOpts := StoreOptions{}
 		systemOpts.GraphDriverName = "btrfs"
diff --git a/types/options_windows.go b/types/options_windows.go
index d44aaf76a3..c1bea9fac0 100644
--- a/types/options_windows.go
+++ b/types/options_windows.go
@@ -12,3 +12,8 @@ const (
 var (
 	defaultOverrideConfigFile = "/etc/containers/storage.conf"
 )
+
+// canUseRootlessOverlay returns true if the overlay driver can be used for rootless containers
+func canUseRootlessOverlay(home, runhome string) bool {
+	return false
+}