diff --git a/homeassistant/components/esphome/ffmpeg_proxy.py b/homeassistant/components/esphome/ffmpeg_proxy.py
index 2dacae52f75..9484d1e7593 100644
--- a/homeassistant/components/esphome/ffmpeg_proxy.py
+++ b/homeassistant/components/esphome/ffmpeg_proxy.py
@@ -212,6 +212,10 @@ class FFmpegConvertResponse(web.StreamResponse):
         assert proc.stdout is not None
         assert proc.stderr is not None
 
+        stderr_task = self.hass.async_create_background_task(
+            self._dump_ffmpeg_stderr(proc), "ESPHome media proxy dump stderr"
+        )
+
         try:
             # Pull audio chunks from ffmpeg and pass them to the HTTP client
             while (
@@ -230,18 +234,14 @@ class FFmpegConvertResponse(web.StreamResponse):
             raise  # don't log error
         except:
             _LOGGER.exception("Unexpected error during ffmpeg conversion")
-
-            # Process did not exit successfully
-            stderr_text = ""
-            while line := await proc.stderr.readline():
-                stderr_text += line.decode()
-            _LOGGER.error("FFmpeg output: %s", stderr_text)
-
             raise
         finally:
             # Allow conversion info to be removed
             self.convert_info.is_finished = True
 
+            # stop dumping ffmpeg stderr task
+            stderr_task.cancel()
+
             # Terminate hangs, so kill is used
             if proc.returncode is None:
                 proc.kill()
@@ -250,6 +250,16 @@ class FFmpegConvertResponse(web.StreamResponse):
             if request.transport and not request.transport.is_closing():
                 await writer.write_eof()
 
+    async def _dump_ffmpeg_stderr(
+        self,
+        proc: asyncio.subprocess.Process,
+    ) -> None:
+        assert proc.stdout is not None
+        assert proc.stderr is not None
+
+        while self.hass.is_running and (chunk := await proc.stderr.readline()):
+            _LOGGER.debug("ffmpeg[%s] output: %s", proc.pid, chunk.decode().rstrip())
+
 
 class FFmpegProxyView(HomeAssistantView):
     """FFmpeg web view to convert audio and stream back to client."""