Barkley has been on the books of Everton his entire professional career so far and has played over 100 Premier League matches.
The 23-year-old attacking midfielder is a very talented and promising footballer, but he has yet to establish himself as one of the very best in the English top flight.
Former Blackburn Rovers striker Sutton believes that Barkley has not progressed as a footballer as he was expected to.
“I don’t think he has kicked on the way everybody thought he would do a few years ago,” Sutton told BT Sport. “It is hard to say he has regressed, but he certainly hasn’t hit the heights, has he?”
Barkley has scored three goals and created 43 chances in 18 Premier League appearances for Everton so far this season.
During the 2015-16 campaign, the England international scored eight goals and created 55 chances in 38 league matches for the Toffees.
Everton are seventh in the Premier League table at the moment with 30 points from 20 matches, 10 points behind fourth-placed Arsenal.
The Merseyside outfit will return to action on Saturday afternoon when they take on Leicester City at Goodison Park in the third round of the FA Cup.