Fellaini's performances led United to trigger the one-year contract extension in his contract at the start of the year – but extending his deal beyond the summer is proving much tougher.
It is understood negotiations with his representatives began last season, with the club still hoping to work through a deal that will extend the Belgium international's stay.
Foreign clubs can agree pre-contract terms with Fellaini from January, with Galatasaray, Besiktas, Valencia and Fenerbache among the clubs to have been linked with a move.
United are understood to be unwilling to sell the midfielder in January so he faces the choice of running down his contact and leaving Old Trafford for free in the summer, or signing a new deal and remaining.
Fellaini put pen to paper on a four-year contract with an option of further year when United forked out £27.5million to sign him in 2013.
Last December, sections of United fans booed the midfielder in their first match back at Old Trafford after he clumsily gave away a penalty which allowed former club Everton to snatch a late draw.
Fellaini has repaid Mourinho's faith with key goals and contributions, while the United boss praised him after returning from a knee injury to feature off the bench in the 1-0 loss at Chelsea before the international break.
"I have to say that Fellaini was fantastic for me, his fellow players, for the fans, for the team, for the club," the United boss said.
"He was injured for weeks, he trained yesterday for the first time with the team and he put himself on the line, ready to come in and help in case the team needed him.
"So I am really pleased with him and I didn't want to go without saying that about Marouane."