The out-of-contract midfielder, currently part of Belgium's World Cup squad, has explained he will announce where his future lies on 1 July.
It seems a strange player to let go, as Jose Mourinho has shown trust in the Belgian, particularly as his alternative plan when the Red Devils are not winning in a game.
The Gunners, AC Milan and Juventus are amongst the clubs interested in signing the 30-year-old on a free with his contract expiration at the end of the month.
Betting company Paddy Power have slashed the odds on a move to the Emirates which is now being priced at 5/6.
Why Arsenal would be a bad option
Arsenal's defensive incapabilities have been ever present over the past few seasons.
The team has been lacking a defensive midfielder and this has cost them heavily.
Fellaini offers an extra dimension in the middle of the park and also for set pieces, however this is not what the Gunners need at the moment.
The Belgian was terrific at Everton and was utilised perfectly at Man United in matches where Mourinho's tactics were not paying dividends.
In the south London club's midfield there is much attacking prowess and creativity but not enough solidarity in the defensive third.
To be able to reach the heights that they were once used to, their scouts need to target a midfielder that can play the role which N'Golo Kante and Nemanja Matic have expertly done for the Blues and the Red Devils respectively.