Arsenal have also been linked with the out-of-favour Spaniard, who has found first team action hard to come by at the Nou Camp this season.
Villa is yet to play a full 90 minutes for Barcelona since returning from a broken leg at the start of the season, prompting rumours that he could be on the move in January.
According to reports in Spain, Villa would be allowed to leave for around €15 million in the new year, with Arsenal and Chelsea particularly in need of a new striker.
The Gunners are on the lookout for more firepower in attack after Robin van Persie's departure in the summer, while Chelsea will also be short of options when Daniel Sturridge completes his much-anticipated move to Liverpool.
However according to the Daily Star, Manchester City are ready enter the race for Villa's signature and steal him from under their rivals noses.
Manchester City boss Roberto Mancini is said to be keen on adding even more firepower in attack in order to help bolster his side's chances of defending their Premier League crown.
Villa is believed to earn wages in the region of £110,000-per-week, a salary that won't be a problem for the Citizens or indeed Chelsea, but one Arsenal could struggle to match.