diff --git a/haystack/components/generators/chat/hugging_face_api.py b/haystack/components/generators/chat/hugging_face_api.py
index 1264272fca..9fb5bda1f3 100644
--- a/haystack/components/generators/chat/hugging_face_api.py
+++ b/haystack/components/generators/chat/hugging_face_api.py
@@ -220,6 +220,7 @@ def run(
         messages: List[ChatMessage],
         generation_kwargs: Optional[Dict[str, Any]] = None,
         tools: Optional[List[Tool]] = None,
+        streaming_callback: Optional[Callable[[StreamingChunk], None]] = None,
     ):
         """
         Invoke the text generation inference based on the provided messages and generation parameters.
@@ -231,6 +232,9 @@ def run(
         :param tools:
             A list of tools for which the model can prepare calls. If set, it will override the `tools` parameter set
             during component initialization.
+        :param streaming_callback:
+            An optional callable for handling streaming responses. If set, it will override the `streaming_callback`
+            parameter set during component initialization.
         :returns: A dictionary with the following keys:
             - `replies`: A list containing the generated responses as ChatMessage objects.
         """
@@ -245,8 +249,9 @@ def run(
             raise ValueError("Using tools and streaming at the same time is not supported. Please choose one.")
         _check_duplicate_tool_names(tools)
 
-        if self.streaming_callback:
-            return self._run_streaming(formatted_messages, generation_kwargs)
+        streaming_callback = streaming_callback or self.streaming_callback
+        if streaming_callback:
+            return self._run_streaming(formatted_messages, generation_kwargs, streaming_callback)
 
         hf_tools = None
         if tools:
@@ -254,7 +259,12 @@ def run(
 
         return self._run_non_streaming(formatted_messages, generation_kwargs, hf_tools)
 
-    def _run_streaming(self, messages: List[Dict[str, str]], generation_kwargs: Dict[str, Any]):
+    def _run_streaming(
+        self,
+        messages: List[Dict[str, str]],
+        generation_kwargs: Dict[str, Any],
+        streaming_callback: Callable[[StreamingChunk], None],
+    ):
         api_output: Iterable[ChatCompletionStreamOutput] = self._client.chat_completion(
             messages, stream=True, **generation_kwargs
         )
@@ -282,7 +292,7 @@ def _run_streaming(self, messages: List[Dict[str, str]], generation_kwargs: Dict
                 first_chunk_time = datetime.now().isoformat()
 
             stream_chunk = StreamingChunk(text, meta)
-            self.streaming_callback(stream_chunk)  # type: ignore # streaming_callback is not None (verified in the run method)
+            streaming_callback(stream_chunk)
 
         meta.update(
             {
diff --git a/haystack/components/generators/chat/hugging_face_local.py b/haystack/components/generators/chat/hugging_face_local.py
index a79a6dcfa8..d5d05ae487 100644
--- a/haystack/components/generators/chat/hugging_face_local.py
+++ b/haystack/components/generators/chat/hugging_face_local.py
@@ -233,12 +233,18 @@ def from_dict(cls, data: Dict[str, Any]) -> "HuggingFaceLocalChatGenerator":
         return default_from_dict(cls, data)
 
     @component.output_types(replies=List[ChatMessage])
-    def run(self, messages: List[ChatMessage], generation_kwargs: Optional[Dict[str, Any]] = None):
+    def run(
+        self,
+        messages: List[ChatMessage],
+        generation_kwargs: Optional[Dict[str, Any]] = None,
+        streaming_callback: Optional[Callable[[StreamingChunk], None]] = None,
+    ):
         """
         Invoke text generation inference based on the provided messages and generation parameters.
 
         :param messages: A list of ChatMessage objects representing the input messages.
         :param generation_kwargs: Additional keyword arguments for text generation.
+        :param streaming_callback: An optional callable for handling streaming responses.
         :returns:
             A list containing the generated responses as ChatMessage instances.
         """
@@ -259,7 +265,8 @@ def run(self, messages: List[ChatMessage], generation_kwargs: Optional[Dict[str,
         if stop_words_criteria:
             generation_kwargs["stopping_criteria"] = StoppingCriteriaList([stop_words_criteria])
 
-        if self.streaming_callback:
+        streaming_callback = streaming_callback or self.streaming_callback
+        if streaming_callback:
             num_responses = generation_kwargs.get("num_return_sequences", 1)
             if num_responses > 1:
                 msg = (
@@ -270,7 +277,7 @@ def run(self, messages: List[ChatMessage], generation_kwargs: Optional[Dict[str,
                 logger.warning(msg, num_responses=num_responses)
                 generation_kwargs["num_return_sequences"] = 1
             # streamer parameter hooks into HF streaming, HFTokenStreamingHandler is an adapter to our streaming
-            generation_kwargs["streamer"] = HFTokenStreamingHandler(tokenizer, self.streaming_callback, stop_words)
+            generation_kwargs["streamer"] = HFTokenStreamingHandler(tokenizer, streaming_callback, stop_words)
 
         hf_messages = [convert_message_to_hf_format(message) for message in messages]
 
diff --git a/releasenotes/notes/streaming-callback-run-param-support-for-hf-chat-generators-68aaa7e540ad03ce.yaml b/releasenotes/notes/streaming-callback-run-param-support-for-hf-chat-generators-68aaa7e540ad03ce.yaml
new file mode 100644
index 0000000000..8d5e6007f5
--- /dev/null
+++ b/releasenotes/notes/streaming-callback-run-param-support-for-hf-chat-generators-68aaa7e540ad03ce.yaml
@@ -0,0 +1,4 @@
+---
+enhancements:
+  - |
+    Streaming callback run param support for HF chat generators.