Reports suggest both City and Arsenal are keen on the frontman, who has struggled to hold down a regular first-team place at Camp Nou this season.
But Arsene Wenger denied any Gunners' interest on Tuesday and Sky Sports understands City are also ruling out a deal.
Roberto Mancini's side appear set to lose striker Mario Balotelli to AC Milan, with the Italian due at the Serie A club for a medical on Wednesday.
However, it seems they will not turn to Villa to fill the void left by the frontman at the Etihad Stadium.
City have also been linked with big-money moves for Napoli striker Edison Cavani and Atletico Madrid's Radamel Falcao.
But manager Mancini has said he does not expect to bring in a replacement for Balotelli before the transfer window closes on Thursday.