The 31-year-old has been with the Old Trafford giants since 2013, with the former Everton midfielder establishing himself as a key figure under Jose Mourinho.
Fellaini was rewarded over the summer with a new and improved deal until 2020, with the option of a further year, but a move to China is now on the cards.
It is understood that Shandong Luneng are in negotiations with United about the permanent transfer of the divisive midfielder.
Another Chinese Super League side are believed to be monitoring the situation, with clubs there having until February 28 to complete signings.
Fellaini has only managed 31 minutes since Ole Gunnar Solskjaer took caretaker charge last month, although a calf injury has ruled him out of recent matches.
Solskjaer said at the start of the week that he did not expect any United exits before Thursday's English transfer deadline and was coy about the Belgium international's future following Tuesday's 2-2 draw with Burnley.
Asked if there was anything he could say on Fellaini, the caretaker manager said: "To be honest, no. I've been busy all day and I don't really know the latest update on that one. Just wait and see."