The Evening Chronicle says the Serbian striker will be told to stay and fight for his place if the price isn't right for his services.
Both Partizan Belgrade and Anderlecht were told last month to forget any chance of signing the striker on loan and return with cash bids if they were keen to re-sign their former player.
Rafa Benitez knows that his own chances of bringing in a striker could depend on Mitrovic being sold in January.
When asked about bringing in a striker, Benitez said: “I can't talk about positions because maybe some players here won't leave.
“I don't have any £15million offers for any of our players at the moment."