Keras Callback to Monitor Both Validation and Training Accuracy at the Same Time
But the model may be overfitted to validation data.

Thats basically not possible. If you split your traing data into validation and training correctly, your model does never see the validation data, before it validates the hypothesis, it learned. 
You can overfit your training data, but you can not overfit your validation data, because the model does not learn, while validating. Thats the idea behind validation split.
I recently came to know about Modelcheckpoint Callback in Keras. But it can only monitor Validation Accuracy or Training Acc. It can save best model weights when validation accuracy is maximum. But the model may be overfitted to validation data. Thus, I feel a need to monitor training accuracy as well. I want to save that model for which Validation Accuracy is maximum and Training Accuracy is also good.
Is there way or callback for it?
Thanks