Tottenham have been monitoring the England man's situation at Goodison Park this summer but have yet to make an official approach to the Merseysiders.
The Blues were believed to want £50m for the 23-year-old, who was told by boss Ronald Koeman he would be sold if he didn't sign a new contract at the end of last season, but so far no-one has met their asking price.
And now the latest reports say Spurs will only offer up to £25m in the hope Everton decide to get rid of a player who is in the last year of his contract and one the manager clearly is keen to dispose of as soon as possible.
It could be that a compromise figure is reached in the region of £30-35m eventually before the transfer window closes at the end of the month but his future remains uncertain.
Chelsea have also been mentioned as possible Barkley suitors as Antonio Conte continues to try and add to his first-team squad but Spurs remain favourites despite a big difference in theirs and Everton's valuation.
Barkley has not featured for the Toffees in pre-season as he's out of favour but he's also been on the sidelines with a groin injury, although he is expected to be back in training next week.