The Spaniard was thought to the be the Gunners' main target over the winter, with Villa also keen on a move to the Emirates Stadium.
However, the Catalan club opted to keep the forward due to their pursuit of the Champions League trophy, according to Mundo Deportivo.
The Spanish newspaper claims that the North Londoners had offered £8.5m for the 31-year-old but the La Liga leaders wanted a larger sum.
Villa, who was eager for a change of scenery and squad role, was willing to negotiate the final part of the fee himself.
Arsenal are thought to still be interested in Villa this summer but face competition from Tottenham Hotspur and Atletico Madrid, with Stevan Jovetic their top target.