Mourinho remains highly keen on the Frenchman who impressed at Euro 2016 and has impressed with Atletico Madrid at the start of the current campaign.
Griezmann pickd up the Golden Boot award at Euro 2016, scoring six goals in seven games for France and has scored nine goals this season.
A move in January appears to be out of the question and the player himself has previously stated that he is happy in the Spanish capital.
However, Griezmann is a close friend of international team-mate Paul Pogba and he may well move to Old Trafford in the summer for a fee of over £60m.