French TV show Foot 365 have stated talks will soon be opened with the giant player - who headed in an injury time victor during April's previous meeting between the Red Devils and Gunners.
Man United manager Jose Mourinho, who is a known fan of Fellaini and would ideally like to keep him around, would be loath to lose the 30-year-old to a Premier League rival.
United have offered Fellaini another 12-month contract extension but the promise of first team football under Emery may be too persuasive.
Metro claim he has already rejected two offers from United and that the Gunners will now meet his representatives this week.More news: French Open 2018: Results, Highlights, Sunday Scores Recap from Roland Garros
More news: Dragon Ball FighterZ and Fortnite Confirmed For Switch?
More news: Singapore will bear some costs of Trump-Kim summit: minister
Fellaini, who made his name at Everton, is now away with Belgium's World Cup squad and is not expected to make any decisions over his future until he returns from Russian Federation next month.
New Arsenal boss Unai Emery was keen on signing Fellaini for Paris Saint-Germain before his departure and has rekindled his interest now he is at the Emirates Stadium.
Arsenal are on a tight budget this summer after spending big on Alexandre Lacazette and Pierre-Emerick Aubameyang last season.