United do not view the Gunners as direct title rivals.
Manchester United are more willing to sell Wayne Rooney to Arsenal than Chelsea, according to the Daily Mirror.
Rooney is set for crunch talks about his future with new United boss David Moyes this week, with both London clubs ready to pounce if the former Everton pair fail to reach an agreement.
It is understood Rooney is angry at his treatment by outgoing Manchester United manager Sir Alex Ferguson, who publicly announced the 27-year-old had handed in a transfer request at Old Trafford.
Moyes will tell the striker that the situation was a misunderstanding and is hopeful of persuading Rooney to remain at the club but is remains likely Rooney will seek a summer exit, with the England international keen to remain in the Premier League despite interest from mega-rich Ligue 1 outfits PSG and AS Monaco.
Both Jose Mourinho and Arsene Wenger are willing to offer Rooney an Old Trafford escape route and the player is interested in teaming up with the Portuguese at Stamford Bridge, where he could play in front of exciting trio Juan Mata, Eden Hazard and Oscar.
But United are reportedly more willing to sell the striker to Arsenal, who they do not believe will be direct rivals for the title next season.