The Blues are keen on strengthening their defensive line this summer, with their frailties at the back underlined by their 3-2 loss to West Ham earlier this week.
A number of targets have so far been identified as potential signings in defence.
According to the Daily Mail, that includes Torres, who has previously been linked with Arsenal, Barcelona, Manchester United and Manchester City.
The 23-year-old has been one of Villarreal’s standout players this season, which is his first full campaign in La Liga.
Whilst he has three years left to run on his contract, he has a release clause of around £45m, which makes him an affordable option for plenty of clubs.
Torres has previously fuelled speculation that his favoured destination was the Premier League, having revealed in April that he was taking English lessons during lockdown.
“In the morning I do the training regime and then I do the food following the guidelines established by the club,” he told El Periodico Mediterraneo.
“In the afternoon, after lunch, I study a few languages because I was learning English and now is a good time to resume it.”
Former Arsenal midfielder Santi Cazorla has previously confirmed that he had spoken to the Gunners about his Villarreal teammate.
“Yeah, mainly my Arsenal friends,” Cazorla told Marca, when asked whether he had spoken to anyone at the Emirates about Torres.
“They ask me about them and they think that they can make the jump to the Premier League soon.
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“It’s good that big clubs are interested in the young players at Villarreal but, for the moment, I’m asking them to let them stay here. They still have to make more steps [in their development].
“Those two have great personalities and their feet are on the ground.
“In Pau’s case, I’m constantly hearing talk about Manchester City or Barcelona, but he knows that he has to keep improving as a player and we’ll see how far he can go in the future.”