Having spent a large amount of money on the likes of Davy Klaassen, Jordan Pickford and Michael Keane, Rooney is hopeful the 23 year-old stays Goodison Park.
"With the ability that Ross has, of course we all want him to be a part of what we're trying to achieve at Everton," Rooney told UK newspapers.
"He can help us get better but the decision about his future is down to him.
"I'm sure he will speak to the manager and do what's right for him."
Rooney is back for his second stint at Everton after spending 13 seasons at Manchester United, where he became the club's record goalscorer.
A 22-time England international, Barkley came through the youth system at Everton.