The 31-year-old striker has been heavily linked with a move to the Premier League after a lack of first-team football in Spain, as Villa continues his rehabilitation from a serious leg injury last season.
Gunners boss Arsene Wenger has been linked with an ambitious bid to bring the Barca star to the Emirates Stadium, while Brendan Rodgers is also believed to be monitoring the former Valencia man's situation, as he too weighs up an attempt to lure the player to Anfield.
However, both Arsenal and Liverpool's hopes of securing Villa's signature in the mid-season transfer window have been dealt a significant blow after Vilanova quashed any possibility of the striker leaving this month.
"David is not going to leave. We are very happy with him," he said, in the aftermath of Barcelona's 3-1 La Liga victory over Malaga last night.
Villa notched a brace in last week's 5-0 Copa del Rey thrashing of Cordoba, showing signs that the Spanish international is starting to get back to his best. However, he limped out of that game in the closing stages, and also picked up a hamstring strain in training which ruled him out of the weekend clash against Malaga.
"The other day he scored two goals," added Vilanova. "We've always said that he's coming off a long injury, and he's getting more minutes all the time. But he's suffering more physical problems again.
"We know how important he is, like last year when we missed him a lot in the second half of the season. I'm convinced he will help us a lot over the remainder of the season."