Unai Emery wants a reunion with the 26-year-old having coached him at the Spanish club.
They won the Europa League together in 2021, beating Manchester United in the final.
Villa are currently in the box seat to land the defender in a £55million deal.
The centre-back has played 23 times for Spain and has 173 appearances for Villarreal since his debut in 2016.
Manchester United and Tottenham have long been linked with Torres, but it appears that Villa could win the race.
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Fernando Roig Negueroles, son of Villarreal's owner, hinted that the club could be forced to sell.
Negueroles said: "Pau is a special case. He is a very loved boy at the club so to leave it has to be something that improves him, something that is good for everyone."
Torres' talent is obvious and easy to see why he has been linked to some of the biggest clubs in Europe.
Former Premier League midfielder Danny Murphy told talkSPORT: "That would be a hell of a signing, by the way. He's a Spanish international and a lovely footballer.
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"He has good size and good presence. I don't know if he plays right or left, so there will be competition for places but you need that."