English publication 'The Express' reports that the Belgian will leave Old Trafford when his contract expires in the summer and that he could be set for a surprise switch to the Emirates.
United are thought to have already offered the 29-year-old a new deal, but despite manager Jose Mourinho's repeated insistence that the midfielder remains a key part of his squad, Fellaini has rejected all offers put to him so far as he searches for more game time and a longer and more lucrative contract.
The aforementioned source claims to have it on good authority that United will resist the urge to cash in on Fellaini in January, meaning that they are resigned to losing him for nothing come the summer.
There is thought to be no shortage of interest in the powerful midfielder, with Besiktas and Inter Milan both thought to be considering moves.
However, the interest from Arsenal comes as something of a surprise, with Fellaini far from a 'typical' Arsenal midfielder.
Fellaini started the season in fine form, scoring four goals in nine games in all competitions before suffering a knee injury on international duty with Belgium. That left him sidelined for a month before he returned to the bench for the defeat to Chelsea just before the international break.
The former Everton man is aware that Paul Pogba's impending return to fitness will limit his first team chances at Old Trafford, though it is possible that he could become a regular fixture for Arsenal.