diff --git a/executor/tiflashtest/tiflash_test.go b/executor/tiflashtest/tiflash_test.go
index 0fd41eb4872cc..e703d66ed33cc 100644
--- a/executor/tiflashtest/tiflash_test.go
+++ b/executor/tiflashtest/tiflash_test.go
@@ -1266,6 +1266,33 @@ func TestGroupStreamAggOnTiFlash(t *testing.T) {
 	}
 }
 
+// TestIssue41014 test issue that can't find proper physical plan
+func TestIssue41014(t *testing.T) {
+	store := testkit.CreateMockStore(t, withMockTiFlash(2))
+	tk := testkit.NewTestKit(t, store)
+	tk.MustExec("use test;")
+	tk.MustExec("CREATE TABLE `tai1` (\n  `aid` int(11) DEFAULT NULL,\n  `rid` int(11) DEFAULT NULL\n) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin")
+	tk.MustExec("CREATE TABLE `tai2` (\n  `rid` int(11) DEFAULT NULL,\n  `prilan` varchar(20) DEFAULT NULL\n) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin")
+	tk.MustExec("alter table tai1 set tiflash replica 1")
+	tk.MustExec("alter table tai2 set tiflash replica 1")
+	tk.MustExec("alter table tai2 add index idx((lower(prilan)));")
+	tk.MustExec("set @@tidb_opt_distinct_agg_push_down = 1;")
+
+	tk.MustQuery("explain select count(distinct tai1.aid) as cb from tai1 inner join tai2 on tai1.rid = tai2.rid where lower(prilan)  LIKE LOWER('%python%');").Check(
+		testkit.Rows("HashAgg_11 1.00 root  funcs:count(distinct test.tai1.aid)->Column#8",
+			"└─HashJoin_15 9990.00 root  inner join, equal:[eq(test.tai2.rid, test.tai1.rid)]",
+			"  ├─Selection_20(Build) 8000.00 root  like(lower(test.tai2.prilan), \"%python%\", 92)",
+			"  │ └─Projection_19 10000.00 root  test.tai2.rid, lower(test.tai2.prilan)",
+			"  │   └─TableReader_18 9990.00 root  data:Selection_17",
+			"  │     └─Selection_17 9990.00 cop[tikv]  not(isnull(test.tai2.rid))",
+			"  │       └─TableFullScan_16 10000.00 cop[tikv] table:tai2 keep order:false, stats:pseudo",
+			"  └─TableReader_23(Probe) 9990.00 root  data:Selection_22",
+			"    └─Selection_22 9990.00 cop[tikv]  not(isnull(test.tai1.rid))",
+			"      └─TableFullScan_21 10000.00 cop[tikv] table:tai1 keep order:false, stats:pseudo"))
+	tk.MustQuery("select count(distinct tai1.aid) as cb from tai1 inner join tai2 on tai1.rid = tai2.rid where lower(prilan)  LIKE LOWER('%python%');").Check(
+		testkit.Rows("0"))
+}
+
 func TestTiflashEmptyDynamicPruneResult(t *testing.T) {
 	store := testkit.CreateMockStore(t, withMockTiFlash(2))
 	tk := testkit.NewTestKit(t, store)
diff --git a/planner/core/exhaust_physical_plans.go b/planner/core/exhaust_physical_plans.go
index a39a14874ce7c..7c0ff0a4274fa 100644
--- a/planner/core/exhaust_physical_plans.go
+++ b/planner/core/exhaust_physical_plans.go
@@ -2790,7 +2790,9 @@ func (la *LogicalAggregation) getStreamAggs(prop *property.PhysicalProperty) []P
 		if la.HasDistinct() {
 			// TODO: remove AllowDistinctAggPushDown after the cost estimation of distinct pushdown is implemented.
 			// If AllowDistinctAggPushDown is set to true, we should not consider RootTask.
-			if !la.ctx.GetSessionVars().AllowDistinctAggPushDown {
+			if !la.ctx.GetSessionVars().AllowDistinctAggPushDown || !la.canPushToCop(kv.TiKV) {
+				// if variable doesn't allow DistinctAggPushDown, just produce root task type.
+				// if variable does allow DistinctAggPushDown, but OP itself can't be pushed down to tikv, just produce root task type.
 				taskTypes = []property.TaskType{property.RootTaskType}
 			} else if !la.distinctArgsMeetsProperty() {
 				continue
@@ -2942,6 +2944,15 @@ func (la *LogicalAggregation) tryToGetMppHashAggs(prop *property.PhysicalPropert
 	return
 }
 
+// getHashAggs will generate some kinds of taskType here, which finally converted to different task plan.
+// when deciding whether to add a kind of taskType, there is a rule here. [Not is Not, Yes is not Sure]
+// eg: which means
+//
+//	1: when you find something here that block hashAgg to be pushed down to XXX, just skip adding the XXXTaskType.
+//	2: when you find nothing here to block hashAgg to be pushed down to XXX, just add the XXXTaskType here.
+//	for 2, the final result for this physical operator enumeration is chosen or rejected is according to more factors later (hint/variable/partition/virtual-col/cost)
+//
+// That is to say, the non-complete positive judgement of canPushDownToMPP/canPushDownToTiFlash/canPushDownToTiKV is not that for sure here.
 func (la *LogicalAggregation) getHashAggs(prop *property.PhysicalProperty) []PhysicalPlan {
 	if !prop.IsSortItemEmpty() {
 		return nil
@@ -2955,7 +2966,9 @@ func (la *LogicalAggregation) getHashAggs(prop *property.PhysicalProperty) []Phy
 	canPushDownToMPP := canPushDownToTiFlash && la.ctx.GetSessionVars().IsMPPAllowed() && la.checkCanPushDownToMPP()
 	if la.HasDistinct() {
 		// TODO: remove after the cost estimation of distinct pushdown is implemented.
-		if !la.ctx.GetSessionVars().AllowDistinctAggPushDown {
+		if !la.ctx.GetSessionVars().AllowDistinctAggPushDown || !la.canPushToCop(kv.TiKV) {
+			// if variable doesn't allow DistinctAggPushDown, just produce root task type.
+			// if variable does allow DistinctAggPushDown, but OP itself can't be pushed down to tikv, just produce root task type.
 			taskTypes = []property.TaskType{property.RootTaskType}
 		}
 	} else if !la.aggHints.preferAggToCop {