The Spain international has been unable to break into the starting line-up under Tito Villanova, which led to speculations linking him with a January exit.
Sport understands that Villa has become fed up with waiting for his chance and met with Catalans boss to inform him of his desire to leave the club in the winter transfer window.
A number of Premier League clubs have expressed their interest in the Spain international, with Arsenal and Liverpool linked with a move for the experienced striker.
Villa, 31, has scored 5 goals in 13 league matches this season, but he only started 6 of those fixtures.
David Villa is still recognized as one of the most prolific strikers in world football, having scored 169 goals in 301 La Liga appearances, while playing for Real Zaragoza, Valencia and Barcelona.