Jack Otway of the Daily Express reported the Belgium international is ready to leave Old Trafford as a free agent, weakening the Special One's midfield options. Roma and Besiktas reportedly want the former Everton player, as Mourinho said he is unsure about Fellaini's intentions.
"Is he going to stay or leave? I don't know, I want him to stay, the club wants him to stay," Mourinho said. "The process, negotiations, numbers, distances between the offer and what he wants, I really don’t know."
Fellaini has been forced out of United's first team due to recent injury, but he emerged last season as one of Mourinho's favoured generals on the pitch. The Belgian was used as an impact player from the bench, but Mourinho's faith in the big man was always evident.
However, the 30-year-old has started just four matches in the Premier League and UEFA Champions League this season, and United have appeared weak in midfield, with Paul Pogba struggling with his coach's tactics and formation.
Pogba needs a dynamic partner in the centre of the park, and when fit, Fellaini is utilised for his height rather than his industry.
In other United news, Juventus general manager Giuseppe Marotta has admitted he is an admirer of Matteo Darmian after the Italian champions were linked with the defender.
Speaking to Calciomercato, Marotta said: "He is a player of Manchester United and is not our property, but he is a good player who interests us."
Darmian appears surplus to requirements at the Theatre of Dreams, and Mourinho has used the Italy international sparingly during his tenure at United.
The former Torino player seemed to have a bright future in his earliest days in Manchester, but his form collapsed in the last 12 months, driving him out of the first-team picture.
United are stacked heavily with defensive options, and with Timothy Fosu-Mensah expected to return from a lengthy loan spell at Crystal Palace in the summer, Darmian is expected to slip further off the radar.
The player was a success in Serie A, and a return to his homeland could trigger a revival in his fortunes.
The Premier League has been too fast and aggressive for his skill set, but he could thrive in a familiar environment.
Juve could provide the perfect answer for the defender, who has seen his stock plummet during his difficult spell in England.