The Manchester Evening News says Manchester United are outright favourites for the Dutch ace.
And he could jet in to sign as early as tonight.
The targetman, who turned 29 on Sunday, was photographed training with his team-mates on Monday in Germany where the Arsenal squad are currently on tour.
They take on FC Cologne on Sunday but it is unlikely van Persie will still be a Gunners player by then.
Arsenal are demanding £25m for van Persie although the final fee is expected to be around £20m.