City are reportedly interested in the young midfielder who has set the Premier League alight in the past year, which also earned him a place in the England squad for the World Cup in Brazil.
But Pearce has pointed to another midfielder in Jack Rodwell who was highly rated and moved to Manchester City, but it didn't work out for him.
Pearce, who previously managed Barkley and Rodwell at England under-21 level, told TalkSport: “Jack Rodwell went to Manchester City and never really featured. He wasted a season or two, instead of playing at Everton a little while longer.
“My advice to Ross would be, ‘sit tight, you’ve got a manager [in Roberto Martinez] who backs good young players’. You’ll always have the option to move away [at a later date] if your form is good.”
Barkley is seen by many as essential to the future of the national side, and when he's fit an integral player in Roberto Martinez's Everton side.
It is easy to see why he would attract the interest of the current Premier League champions. He has an excellent technique, pace, power and end product. He would fit into any side very well.
Rodwell and Barkley are very different players, but Rodwell's career should act as a warning if City come calling. Rodwell was tipped for big things but rarely played, and is now playing for Sunderland. It could have been very different for him if he stayed at Goodison Park and developed more before leaving for the Etihad Stadium.