SunSport understands he is keener on moving to the Emirates than Liverpool or staying at Man City.
The England midfielder, 29, is out of contract this summer and has refused to sign a new deal.
Despite making 40 appearances for City this season, he is frustrated at spending time on the bench and not playing in a settled position in midfield.
Gunners boss Arsene Wenger rates Milner as one of the best players in the Premier League.
And the prospect of regular football in his best position looks like sealing the deal.
Milner can move for free at the end of this season, having joined City for £26million from Aston Villa in 2010.
The offer of a £130k-a-week deal makes the move very tempting.
If he goes to north London, it would once again put the future of Jack Wilshere in doubt.
He has been touted as a target for City and Arsenal may cash in.