diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 182938c9092..bebed5993c6 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -2602,26 +2602,25 @@ def report(self, msg, ts=None, client=None):
         If the message contains a key then we only send the message to those
         comms that care about the key.
         """
-        comms = set()
-        if client is not None:
-            try:
-                comms.add(self.client_comms[client])
-            except KeyError:
-                pass
-
         if ts is None and "key" in msg:
             ts = self.tasks.get(msg["key"])
+
         if ts is None:
             # Notify all clients
-            comms.update(self.client_comms.values())
-        else:
+            client_keys = list(self.client_comms)
+        elif client is None:
             # Notify clients interested in key
-            comms.update(
-                self.client_comms[c.client_key]
-                for c in ts.who_wants
-                if c.client_key in self.client_comms
-            )
-        for c in comms:
+            client_keys = [c.client_key for c in ts.who_wants]
+        else:
+            # Notify clients interested in key (including `client`)
+            client_keys = [c.client_key for c in ts.who_wants if c.client_key != client]
+            client_keys.append(client)
+
+        for k in client_keys:
+            try:
+                c = self.client_comms[k]
+            except KeyError:
+                continue
             try:
                 c.send(msg)
                 # logger.debug("Scheduler sends message to client %s", msg)