The 20-year-old is said to be attracting the attention of the champions, but Pearce has doubts about a move to the Etihad next summer.
The ex-England Under-21 boss used former Everton midfielder Jack Rodwell as an example of how a switch to City does not always work out for talented youngsters.'
He told talkSPORT: "Jack Rodwell went to Manchester City and never really featured.
"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 currently out injured with a knee problem.