diff --git a/src/net/http/transport.go b/src/net/http/transport.go
index 35dfe908d825f4..c2376aa6615aea 100644
--- a/src/net/http/transport.go
+++ b/src/net/http/transport.go
@@ -2267,6 +2267,7 @@ func (pc *persistConn) readLoop() {
 			pc.t.cancelRequest(rc.cancelKey, rc.req.Context().Err())
 		case <-pc.closech:
 			alive = false
+			pc.t.setReqCanceler(rc.cancelKey, nil)
 		}
 
 		testHookReadLoopBeforeNextRead()
diff --git a/src/net/http/transport_test.go b/src/net/http/transport_test.go
index bcc26aa58e03fa..4ff26ff32af00a 100644
--- a/src/net/http/transport_test.go
+++ b/src/net/http/transport_test.go
@@ -6810,3 +6810,55 @@ func testRequestSanitization(t *testing.T, mode testMode) {
 		resp.Body.Close()
 	}
 }
+
+// Issue 61708
+func TestTransportAndServerSharedBodyReqCancelerCleanupOnConnectionClose(t *testing.T) {
+	run(t, testTransportAndServerSharedBodyReqCancelerCleanupOnConnectionClose, []testMode{http1Mode})
+}
+func testTransportAndServerSharedBodyReqCancelerCleanupOnConnectionClose(t *testing.T, mode testMode) {
+	const bodySize = 1 << 20
+
+	backend := newClientServerTest(t, mode, HandlerFunc(func(rw ResponseWriter, req *Request) {
+		io.Copy(rw, req.Body)
+	}))
+	t.Logf("Backend address: %s", backend.ts.Listener.Addr().String())
+
+	var proxy *clientServerTest
+	proxy = newClientServerTest(t, mode, HandlerFunc(func(rw ResponseWriter, req *Request) {
+		breq, _ := NewRequest("POST", backend.ts.URL, req.Body)
+
+		bresp, err := backend.c.Do(breq)
+		if err != nil {
+			t.Fatalf("Unexpected proxy outbound request error: %v", err)
+		}
+		defer bresp.Body.Close()
+
+		_, err = io.Copy(rw, bresp.Body)
+		if err == nil {
+			t.Fatalf("Expected proxy copy error")
+		}
+		t.Logf("Proxy copy error: %v", err)
+	}))
+	t.Logf("Proxy address: %s", proxy.ts.Listener.Addr().String())
+
+	req, _ := NewRequest("POST", proxy.ts.URL, io.LimitReader(neverEnding('a'), bodySize))
+	res, err := proxy.c.Do(req)
+	if err != nil {
+		t.Fatalf("Original request: %v", err)
+	}
+	// Close body without reading to trigger proxy copy error
+	res.Body.Close()
+
+	// Verify no outstanding requests after readLoop/writeLoop
+	// goroutines shut down.
+	waitCondition(t, 10*time.Millisecond, func(d time.Duration) bool {
+		n := backend.tr.NumPendingRequestsForTesting()
+		if n > 0 {
+			if d > 0 {
+				t.Logf("pending requests = %d after %v (want 0)", n, d)
+			}
+			return false
+		}
+		return true
+	})
+}