However, the 29-year-old Milner, who becomes a free agent when his City contract expires this summer, will not make a decision about his future until after the upcoming England games.
Milner has 53 caps to his name and is in the squad once again for the friendly against Republic of Ireland (June 7) and the Euro 2016 qualifier in Slovenia (June 14).
The versatile Milner featured regularly for Manchester City last season and the Premier League second-place finishers are believed to have offered him improved terms to stay with the club.
But he started just 18 of the 32 Premier League games he appeared in last term and it has been suggested that he would be interested in a move to a club where he would be a regular starter.
He has been at Manchester City since the summer of 2010 but has been linked with a switch to Liverpool for a while and it seems that FA Cup winners Arsenal are also now contenders for his signature.
Even in slightly limited action, Milner managed seven Premier League assists last season and scored five times into the bargain.