Fabregas has been repeatedly linked with a move to Manchester United, who failed in their attempts to secure his services before the start of the current season.
United are believed to still be interested in the Spaniard, but The Express reports that they could face competition from their fierce rivals.
Despite being jeered by some of the club's supporters recently, Fabregas has not yet indicated that he would be willing to return to the Premier League.
The 26-year-old's future could depend on whether Barcelona are successful in signing Arturo Vidal, who is believed to be a top target for the club, and any possible move could see City prepare a bid for the former Arsenal midfielder.
Fabregas joined Barcelona from the Gunners in the summer of 2011.