The newspaper claim on their website that Tottenham are also interested in a three-horse Premier League race for the Spanish international enforcer.
The Mirror report that Llorente has a release clause of £45million, but Sociedad are suggested to not be under any financial pressure to sell the 26-year-old.
Llorente has played 10 times for the Spaniards this season already, with nine appearances in La Liga and the singular game in the Copa del Rey, including three cleans – one of those against Atletico Madrid.
Looking at the way the Premier League table and the start of the season, the most attractive of the moves for Llorente to make would be to Leicester. West Ham would need to present a project for the Spaniard that would make him want to make the move to East London, and the best way to do that would be for them to show ambition to secure a European spot. The Hammers are currently going backwards at this moment under Manuel Pellegrini, and bringing in a big-money name like Llorente could certainly act as a catalyst to set them on their way in the second-half of the season. The 26-year-old has enjoyed a solid start to the season in La Liga, and although he most likely would have liked to have kept more clean sheets, he can not be blamed for that. Llorente is averaging 3.8 clearances per game according to WhoScored – which is similar to Issa Diop and only Angelo Ogbonna has completed significantly more.