The Bulgaria international is a free agent after he was released by City at the end of the season.
A host of Premier League clubs including Aston Villa, Bolton, West Ham and Newcastle have all been linked, along with Scottish giants Celtic.
However, it is understood that Everton have already made moves to persuade Petrov that he should make the switch to Merseyside.
Petrov, who was with City for three years after leaving Atletico Madrid, is reportedly settled in the North West and Everton hope that will help them seal a deal.
Source: Team Talk
Source: Team Talk