Everton want star man Barkley to sign a new contract to stop him leaving for a rival club.
But the Daily Star Sunday claim Barkley has delayed his decision over the deal as he keeps his options open.
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?
And it has left Everton manager Ronald Koeman sweating over his star man.
It is claimed Barkley, who does not have the best of relationships with Dutchman Koeman, is in no rush to sign an improved contract on Merseyside.
That is despite the playmaker having less than 18 months left on his current £65,000-a-week deal.
Spurs were linked with a move for Barkley during the January transfer window but Everton were in no mood to sell their academy product.
Reports claim Arsenal, Man Utd, City, Chelsea and Spurs want to sign Ross Barkley
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Barkley has scored five goals for Everton this season
Barkley's (right) contract expires in the summer of 2018
The youngster has scored five goals for Everton this season but was unable to help the Toffees past Middlesbrough in their goalless draw at the Riverside yesterday.
Manchesters United and City were supposedly interested in Barkley last summer before moving for different midfield options.
The report adds that Barkley will also have a number of suitors from across Europe when he comes to make his decision at the end of the season.