The midfielder has been told he does not figure in Barcelona's plans and is available for transfer - they want to replace him with Atletico Madrid midfielder Koke.
Manchester United and Chelsea are among the clubs thought to be interested but City have other targets with defensive players a priority.
Spanish football expert Guillem Balague told Sky Sport News that Barca are keen to offload Fabregas - but that he will not be returning to Arsenal.
"They have told Fabregas to look for a team - but Arsenal are not interested," he said.
"Barca want at least 35m euros - he cost 40m - I think (Barca coach) Luis Enrique has concluded the way he played at Arsenal, he cannot play like that at Barca because it's a more tactically disciplined team.
"Fabregas came to Barcelona and expected something else but what he saw was fans who weren't all happy that he'd cost 40m euros having been developed at La Masia (Barcelona's academy).
"But his stats were really good - he just didn't have the unanimous love of the fans.
"There was a story in one of the Catalan papers on Monday afternoon saying that Chelsea and him have agreed to a deal - that's not true - not yet anyway - but Chelsea are a team would suit him, as would Manchester United.
It is understood that Fabregas has a £30million release clause written into the five-year contract he signed in 2011, describing the move at the time as the "greatest challenge of his life".