The Manchester City midfielder is out of contract at the end of the season and has been linked with both the Gunners and the Reds.
Manuel Pellegrini is keen to keep Milner at the Etihad but reports now suggest that the England international will turn his back on the Premier League.
According to ESPN FC, Milner has his heart set on trying his luck in another league.
There is reportedly interest from a number of foreign clubs and Milner is said to have wanted to play abroad for some time.
The 29-year-old has been learning Spanish and has picked up bits of other languages over the course of his career with Leeds, Aston Villa, Newcastle and City.
GETTY
James Milner is keen to play abroad
It's very difficult to find another Milner - an intelligent player, with big balls and a massive heart.
Manuel Pellegrini
Pellegrini stated this week that Milner would be very difficult to replace should he leave, saying: "It would be very difficult to find a more complete player than Milner.
"There are players who are better technically. There are quicker players. There are players who head the ball better.
"But show me a player who does all the things that Milner does well and there isn't one. And whatever position I put him in he plays well.
"It's very difficult to find another Milner - an intelligent player, with big balls and a massive heart."
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
