The Everton midfielder's future is uncertain with his contract up in 15 months.
Ronald Koeman admitted last week that he would be sold this summer unless he agreed an extension.
And a number of top clubs are considering moves for the 23-year-old.
Ross Barkley is ready to move down south to London
Ross Barkley is attracting interest from Arsenal, Chelsea and Tottenham
And the Evening Standard report that Barkley is ready to pack his bags for London this summer.
Tottenham are believed to be leading the race for his signature but they will face competition from their two city rivals.
The midfielder is back in the England squad this week and could play against Germany tomorrow night after impressing in recent weeks.
England are without Jordan Henderson, Jack Wilshere and Wayne Rooney, meaning there may be a spot for Barkley in the starting XI.
Ross Barkley's horror tackle on Jordan Henderson during Merseyside derby
Tue, December 20, 2016
Should Ross Barkley have been sent off for his horror tackle on Jordan Henderson during the Merseyside derby
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Should Ross Barkley have been sent off for this horror tackle on Jordan Henderson?
His relationship with Toffees boss Koeman is frosty after the Dutchman's tough love approach to bring the best out of him.
But last week he claimed he may have to move the academy product on.
"Ross is a boy from Everton and what we need to show for him is the best reasons to stay and of course his situation is different because his (contract) is running out next season," said Koeman.
"Football is a business and you make decisions at the end of the season.
"He needs to sign a new contract, if not you need to sell the player.
"It is not an ultimatum but that is normal – that is business.
"When I was manager at Southampton we had (Nathaniel) Clyne and he did not accept a new contract so we sold him in the summer.
"I spoke to Ross about a new contract and now it is up to the board to get that contract over the line.
"The player has to understand if he does not sign a new contract by one year (left) you need to make a decision for the club so it knows what will happen next year.
"Ultimatum is strong, I don't like that word, it's not like that."