The England international attacking midfielder has been linked with a move away from the Merseyside outfit in the summer transfer window.
According to The Mirror, Tottenham Hotspur are interested in signing the 23-year-old and will try to secure his services before they leave for their pre-season tour of the USA.
Rooney, who recently returned from Everton from Manchester United, has suggested that he wants Barkley to remain at Goodison Park for the 2017-18 campaign.
“With the ability that Ross has, we all want him to be a part of what we’re trying to achieve at Everton,” Rooney told The Mirror about Barkley.
“But the decision about his future is down to him and I’m sure he’ll speak to the manager and do what’s right.”
Given the signings that Everton have already made in the summer transfer window so far, Barkley could find it hard to play regularly for the Toffees next season.
However, Tottenham have some wonderful midfielders as well, and the Englishman would have to work hard in order to cement a place in Mauricio Pochettino’s starting lineup.