After arriving on loan in the summer, Muniz featured regularly for Middlesbrough but recently has found it harder to get into the team.
He has not made a single appearance in the Championship this year and has failed to even make the squad in the last three games.
Muniz came to Middlesbrough on what was intended to be a season-long loan but Boro are of a different mind.
Middlesbrough want Muniz to go back to Fulham and end his loan spell and they are discussing with the London club over the possibility.
Fulham themselves do not want Muniz to miss first-team action but he is not in the picture to be in the senior team at Craven Cottage.
The Cottagers want the striker to go on loan to the Championship again should he exit Middlesbrough, but there are no offers at this stage for him.
Fulham do not want to send him on loan abroad, but they have discussed the Middlesbrough misfit with a few European clubs and could turn to them as an option.