Additionally, Manchester United are set to bid for the Spaniard before the end of the window, with their interest in him increasing after he was part of the Villarreal side that beat them in the UEFA Europa League final last month.
With Sergio Ramos leaving Real Madrid, the Spanish side need a player to fill that role, but they are working on a limited budget, and so signing Torres seems out of their plans.
The report adds that United see Torres as the ideal player to partner Harry Maguire, in terms of his price, his age, and also with his overall performances for the Spanish side.
Torres played in 44 games for Villarreal in all competitions, even scoring three goals and providing two assists, as the Spanish side finished seventh in La Liga and won the Europa League.
Real Madrid are still interested in a move for him in the future, but not for this summer, as they seek to raise funds from player sales.
With Real Madrid out of the race for this summer, United are the clear favourites to sign the 24-year-old, who is valued at €50 million (transfermarkt.com), but Villarreal will most likely demand an even higher fee than it given that he has a contract with the club until 2024.