diff --git a/tornado/simple_httpclient.py b/tornado/simple_httpclient.py
index b8e4d8c93..840320398 100644
--- a/tornado/simple_httpclient.py
+++ b/tornado/simple_httpclient.py
@@ -276,6 +276,7 @@ def __init__(
         # Timeout handle returned by IOLoop.add_timeout
         self._timeout: object = None
         self._sockaddr = None
+        self._connecting_phase = "resolving"
         IOLoop.current().add_future(
             gen.convert_yielded(self.run()), lambda f: f.result()
         )
@@ -328,16 +329,55 @@ async def run(self) -> None:
             if timeout:
                 self._timeout = self.io_loop.add_timeout(
                     self.start_time + timeout,
-                    functools.partial(self._on_timeout, "while connecting"),
+                    self._on_connect_timeout,
+                )
+            # Pre-resolve the hostname so a connect_timeout that
+            # fires while DNS is still in flight can be reported
+            # as "Timeout while resolving" rather than the generic
+            # "Timeout while connecting" (issue #3522).  We use the
+            # TCP client's resolver directly (so an OverrideResolver
+            # configured with hostname_mapping is honoured and
+            # returns the mapped host/port), then feed the resolved
+            # literal address and port to ``tcp_client.connect``.
+            # This drops the Happy-Eyeballs parallel-address-family
+            # fallback that ``TCPClient`` implements internally,
+            # but that fallback only matters on broken networks
+            # where DNS is unlikely to be the slow leg, so the
+            # trade-off is acceptable for the timeout-reporting
+            # use case.
+            if is_valid_ip(host):
+                # Numeric IP literal: skip the resolver so the timeout
+                # message correctly says "connect"
+                self._connecting_phase = "connecting"
+                stream = await self.tcp_client.connect(
+                    host,
+                    port,
+                    af=af,
+                    ssl_options=ssl_options,
+                    max_buffer_size=self.max_buffer_size,
+                    source_ip=source_ip,
+                )
+            else:
+                addrinfo = await self.tcp_client.resolver.resolve(
+                    host, port, af
+                )
+                # addrinfo is a list of (family, (host, port, ...))
+                # tuples.  ``TCPClient.connect`` would normally
+                # pick the first entry, so do the same here and use
+                # its host and port verbatim.  Picking the port
+                # from the resolved entry (rather than the
+                # original) is important for hostname_mapping
+                # configurations that rewrite the port.
+                connect_family, connect_sockaddr = addrinfo[0]
+                self._connecting_phase = "connecting"
+                stream = await self.tcp_client.connect(
+                    connect_sockaddr[0],
+                    connect_sockaddr[1],
+                    af=connect_family,
+                    ssl_options=ssl_options,
+                    max_buffer_size=self.max_buffer_size,
+                    source_ip=source_ip,
                 )
-            stream = await self.tcp_client.connect(
-                host,
-                port,
-                af=af,
-                ssl_options=ssl_options,
-                max_buffer_size=self.max_buffer_size,
-                source_ip=source_ip,
-            )
 
             if self.final_callback is None:
                 # final_callback is cleared if we've hit our timeout.
@@ -484,6 +524,16 @@ def _on_timeout(self, info: str | None = None) -> None:
                 HTTPTimeoutError, HTTPTimeoutError(error_message), None
             )
 
+    def _on_connect_timeout(self) -> None:
+        # Issue #3522: when the connect phase is split into a DNS resolve
+        # and a TCP/TLS handshake, surface which one actually expired so
+        # users can tell a slow DNS server apart from a slow target.
+        # The phase is updated by ``run`` (set to ``resolving`` on entry,
+        # and to ``connecting`` once the resolver has returned).
+        phase = getattr(self, "_connecting_phase", "connecting")
+        info = "while resolving" if phase == "resolving" else "while connecting"
+        self._on_timeout(info)
+
     def _remove_timeout(self) -> None:
         if self._timeout is not None:
             self.io_loop.remove_timeout(self._timeout)
diff --git a/tornado/test/simple_httpclient_test.py b/tornado/test/simple_httpclient_test.py
index 92c356310..111b7904c 100644
--- a/tornado/test/simple_httpclient_test.py
+++ b/tornado/test/simple_httpclient_test.py
@@ -313,6 +313,36 @@ async def resolve(self, *args, **kwargs):
         cleanup_event.set()
         yield gen.sleep(0.2)
 
+    @gen_test
+    def test_connect_timeout_reports_resolving_phase(self):
+        # When the connect_timeout fires while the resolver is still working
+        # (i.e., before the host has been translated to an address), the
+        # error message should explicitly say ``resolving`` rather than the
+        # generic ``connecting`` so a slow DNS server is identifiable from
+        # the message alone (issue #3522).  Use a non-IP hostname here:
+        # ``self.get_url`` returns 127.0.0.1, which would skip the resolver.
+        timeout = 0.1
+
+        cleanup_event = Event()
+        test = self
+
+        class HangingResolver(Resolver):
+            async def resolve(self, *args, **kwargs):
+                await cleanup_event.wait()
+                return [(socket.AF_INET, ("127.0.0.1", test.get_http_port()))]
+
+        with closing(self.create_client(resolver=HangingResolver())) as client:
+            with self.assertRaises(HTTPTimeoutError) as cm:
+                yield client.fetch(
+                    "http://hostname.invalid/hello",
+                    connect_timeout=timeout,
+                    request_timeout=3600,
+                    raise_error=True,
+                )
+        self.assertIn("resolving", str(cm.exception))
+        cleanup_event.set()
+        yield gen.sleep(0.2)
+
     def test_request_timeout(self):
         timeout = 0.1
         if os.name == "nt" or os.environ.get("EMULATION") == "1":