The academy graduate has failed to truly hit the levels that many expected of him when first breaking into the first team seven years ago, racking up 179 senior appearances and scoring 27 goals during that time.
Barkley's reluctance to put pen to paper on a new contract leaves him open to depart as a free agent next summer, with boss Ronald Koeman confessing earlier this week that the situation remains unclear.
Rooney, who returned to Goodison Park last week after being allowed to leave Manchester United, claims that it is important Everton keep hold of the England midfielder.
"With the ability that Ross has, we all want him to be a part of what we're trying to achieve at Everton," he told reporters. "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.
"Everton have always had ambition, but I feel the club didn't really push on with that ambition. But now they are starting to act on that ambition and as a fan it's great to see.
"To come back here and try to help with that was perfect for me. I'll be trying to help the young lads to get the best out of them."