The Spain international is currently at the World Cup in Qatar, as part of Luis Enrique’s 26-man squad.
However, reports surfaced linking him with a move to Premier League giants Liverpool, who are allegedly in the market for a new midfielder due to long-term injuries suffered by Arthur Melo and Naby Keita.
The Reds manager Jurgen Klopp is reportedly a fan of Llorente, whose deal runs out in 2027.
The 27-year-old has been a key figure for Los Rojiblancos so far this season, where he has managed to score one goal in 12 appearances.
Llorente will be available for a fee of around €40m and the Merseyside club are stated to be willing to table an offer of that size.