Mikel Arteta may lose out-of-contract duo Alexandre Lacazette and Eddie Nketiah at the end of the season, and the Gunners need reinforcements in the attacking department.
Rashford has fallen down the pecking order at United, starting just three league games since the turn of the year, and was left out of Gareth Southgate's England squad.
And according to The Mirror, Arsenal could offer Rashford respite as they consider making an offer for the 24-year-old, who has just one year left on his current deal at Old Trafford.
The report adds that Arteta's side will make an offer for Rashford if they secure Champions League football this season.
The 2022 World Cup is just eight months away, and if Rashford hopes to break into Southgate's squad, he will need to find his form again and start racking up regular playing minutes.
Football Insider have claimed that Rashford has told friends he wants to leave United as he looks to reingite his career.