Manchester United are yet to comment on the extent of the injury, but it is expected to hit the club's intention to off-load the midfielder to the Italian Serie A side before the end of the transfer window.
Photographs of Fellaini in The Sun showed the 26-year-old on crutches with his left foot in a protective cast.
New United boss Louis Van Gaal has made it clear he does not see a future for Fellaini at Old Trafford despite mounting injury problems at the club.
Fellaini's midfield partner Michael Carrick is already ruled out for around two months with an ankle injury, leaving Ander Herrera, Tom Cleverley and Darren Fletcher as United's only fit central midfielders.
Fellaini has endured a disappointing career at Old Trafford since his £27.5million move from Everton on transfer deadline day last summer.
He was booed by some United fans during the pre-season win over Valencia but also scored the winning goal.
Fellaini also appeared as a substitute in Saturday's Barclays Premier League defeat to Swansea, replacing Herrera for the last 23 minutes of the match.