Left-back Baines has been heavily linked to follow former Toffees manager David Moyes to Premier League champions Manchester United, but Barkley is hoping that one of his 'role models' remains at Goodison Park.
"I've been following what is happening at Everton and I desperately want Leighton to stay," Sky Sports News quotes Barkley as saying.
"He's someone I look up to, a role model in how he conducts himself and the strides he has made in his career."
Barkley is currently on duty with England's Under-20 side at the World Cup in Turkey. They face Egypt tonight at 7pm and have to win to stand a chance of qualifying for the knockout stages.