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Spanish radio station Cadena COPE report Barca called Villarreal last week to make an enquiry about the highly-rated 23-year-old centre back.
Torres signed a new Villarreal contract until 2024 last Autumn with a €50m release clause which could total €75m including bonuses.
Villarreal president Fernando Roig reportedly "loves" Torres and does not want to sell him. Torres made 34 appearances for Villarreal last season.
The 19/20 La Liga runners-up are looking for an alternative centre back option who can provide competition with Samuel Umtiti, Clement Lenglet and Gerard Pique.
Barcelona are also linked to Manchester City's 19-year-old centre back Eric Garcia.
The Spanish centre back, who came through La Masia academy before joining City in 2017, has impressed in the Premier League - making 13 league appearances during the 19/20 season.
Eric Garcia, Manchester City
According to Mundo Deportivo on Monday, the Spain U21 international is being considered as a long-term option.
Barcelona would apparently also consider bringing him in on a free next season.
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