Barca and Arsenal have made contact with United during the international break to register their interest in the France international.
While the response to Arsenal has been negative, Mourinho has suggested a price to Barca, says Diario Gol.
It's suggested Mourinho has responded to Barca's enquiry by insisting on midfielder Ivan Rakitic as part of a swap.
Mourinho is a big fan of the Croatia international and at 30 believes he can offer stability and experience to United's midfield, particularly with Michael Carrick likely to leave at the end of the season.
Barca could be willing to do business if they can secure Schalke's Bosman prospect Leon Goretzka to a pre-contract in the New Year.