Barton is wanted by Roma, Atletico Madrid, Hamburg or Bayern Munich, says The Sun.
The 24-year-old midfielder is hoping a move abroad will will give him the chance of salvaging his career.
But it is believed Everton and Newcastle are still leading the race to sign Barton.
A source close to the player told The Sun: “Joey doesn’t want to give up on his England career. He’d love to stay at City but that door now seems closed.
“The club will accept the £5.5million buyout clause in his contract.
“The opportunity to play overseas will take him out of the spotlight in the UK.
“He is desperate to focus on his football away from outside influences.
“And he sees Owen Hargreaves’ development at Bayern Munich as proof his England career could be salvaged by playing abroad.”