The Portuguese manager, prior to the end of the Premier League season, had mentioned his confidence over Fellaini's future, but the midfielder is set to enter fresh contract talks.
The Belgium global is out of contract after five years at Old Trafford and free to negotiate with interested clubs.
Metro claim he has already rejected two offers from United and that the Gunners will now meet his representatives this week.
United have reportedly offered Fellaini a new deal but a lack of playing time will nearly certainly force him to move on.
Fellaini, who is part of Belgium's World Cup squad, joined United from Everton in 2013 but has failed to hold down a regular place in recent times.
It is believed new Arsenal boss Unai Emery had been keen to sign the Belgium global when he was Paris Saint Germain manager and his representatives are due to meet with club officials this week.
Arsenal have both Jack Wilshere and Santi Cazorla out of contract this summer, with the latter signing for Villareal which means midfield recruitments are necessary going into the 2018/19 season.
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