diff --git a/daemon/stop.go b/daemon/stop.go
index 5a659c1cc8..0d29e5c996 100644
--- a/daemon/stop.go
+++ b/daemon/stop.go
@@ -36,7 +36,13 @@ func (daemon *Daemon) ContainerStop(ctx context.Context, name string, options co
 }
 
 // containerStop sends a stop signal, waits, sends a kill signal.
-func (daemon *Daemon) containerStop(ctx context.Context, ctr *container.Container, options containertypes.StopOptions) (retErr error) {
+func (daemon *Daemon) containerStop(_ context.Context, ctr *container.Container, options containertypes.StopOptions) (retErr error) {
+	// Deliberately using a local context here, because cancelling the
+	// request should not cancel the stop.
+	//
+	// TODO(thaJeztah): pass context, and use context.WithoutCancel() once available: https://github.com/golang/go/issues/40221
+	ctx := context.Background()
+
 	if !ctr.IsRunning() {
 		return nil
 	}
diff --git a/integration/container/stop_linux_test.go b/integration/container/stop_linux_test.go
index 0535ce7787..9cfe42351d 100644
--- a/integration/container/stop_linux_test.go
+++ b/integration/container/stop_linux_test.go
@@ -1,8 +1,10 @@
 package container // import "github.com/docker/docker/integration/container"
 
 import (
+	"bytes"
 	"context"
 	"fmt"
+	"io"
 	"strconv"
 	"strings"
 	"testing"
@@ -10,8 +12,12 @@ import (
 
 	"github.com/docker/docker/api/types"
 	containertypes "github.com/docker/docker/api/types/container"
+	"github.com/docker/docker/client"
+	"github.com/docker/docker/errdefs"
 	"github.com/docker/docker/integration/internal/container"
+	"github.com/docker/docker/pkg/stdcopy"
 	"gotest.tools/v3/assert"
+	is "gotest.tools/v3/assert/cmp"
 	"gotest.tools/v3/icmd"
 	"gotest.tools/v3/poll"
 	"gotest.tools/v3/skip"
@@ -98,3 +104,77 @@ func TestDeleteDevicemapper(t *testing.T) {
 	err = client.ContainerRemove(ctx, id, types.ContainerRemoveOptions{})
 	assert.NilError(t, err)
 }
+
+// TestStopContainerWithTimeoutCancel checks that ContainerStop is not cancelled
+// if the request is cancelled.
+// See issue https://github.com/moby/moby/issues/45731
+func TestStopContainerWithTimeoutCancel(t *testing.T) {
+	t.Parallel()
+	defer setupTest(t)()
+	apiClient := testEnv.APIClient()
+	t.Cleanup(func() { _ = apiClient.Close() })
+
+	ctx := context.Background()
+	id := container.Run(ctx, t, apiClient,
+		container.WithCmd("sh", "-c", "trap 'echo received TERM' TERM; while true; do usleep 10; done"),
+	)
+	poll.WaitOn(t, container.IsInState(ctx, apiClient, id, "running"))
+
+	ctxCancel, cancel := context.WithCancel(context.Background())
+	t.Cleanup(cancel)
+	const stopTimeout = 3
+
+	stoppedCh := make(chan error)
+	go func() {
+		sto := stopTimeout
+		stoppedCh <- apiClient.ContainerStop(ctxCancel, id, containertypes.StopOptions{Timeout: &sto})
+	}()
+
+	poll.WaitOn(t, logsContains(ctx, apiClient, id, "received TERM"))
+
+	// Cancel the context once we verified the container was signaled, and check
+	// that the container is not killed immediately
+	cancel()
+
+	select {
+	case stoppedErr := <-stoppedCh:
+		assert.Check(t, is.ErrorType(stoppedErr, errdefs.IsCancelled))
+	case <-time.After(5 * time.Second):
+		t.Fatal("timeout waiting for stop request to be cancelled")
+	}
+	inspect, err := apiClient.ContainerInspect(ctx, id)
+	assert.Check(t, err)
+	assert.Check(t, inspect.State.Running)
+
+	// container should be stopped after stopTimeout is reached. The daemon.containerStop
+	// code is rather convoluted, and waits another 2 seconds for the container to
+	// terminate after signaling it;
+	// https://github.com/moby/moby/blob/97455cc31ffa08078db6591f018256ed59c35bbc/daemon/stop.go#L101-L112
+	//
+	// Adding 3 seconds to the specified stopTimeout to take this into account,
+	// and add another second margin to try to avoid flakiness.
+	poll.WaitOn(t, container.IsStopped(ctx, apiClient, id), poll.WithTimeout((3+stopTimeout)*time.Second))
+}
+
+// logsContains verifies the container contains the given text in the log's stdout.
+func logsContains(ctx context.Context, client client.APIClient, containerID string, logString string) func(log poll.LogT) poll.Result {
+	return func(log poll.LogT) poll.Result {
+		logs, err := client.ContainerLogs(ctx, containerID, types.ContainerLogsOptions{
+			ShowStdout: true,
+		})
+		if err != nil {
+			return poll.Error(err)
+		}
+		defer logs.Close()
+
+		var stdout bytes.Buffer
+		_, err = stdcopy.StdCopy(&stdout, io.Discard, logs)
+		if err != nil {
+			return poll.Error(err)
+		}
+		if strings.Contains(stdout.String(), logString) {
+			return poll.Success()
+		}
+		return poll.Continue("waiting for logstring '%s' in container", logString)
+	}
+}