The 33-year-old Spaniard is up for grabs after failing to impress Mauricio Pochettino and the Hammers are looking to bring him in to add more depth to their attack.
With the likes of Andy Carroll injured and Hugill on loan, Pellegrini needs to add a striker to his squad. Llorente could prove to be a good short-term option.
Llorente could be the ideal alternative for Chicharito next season. It will be interesting to see whether the Hammers can agree on a deal with their London rivals now.
Tottenham have failed to sign anyone this summer and losing Llorente now would only weaken the squad. The Spaniard is their only alternative to Harry Kane.
Even though the Spaniard has been a disappointment for Spurs so far, they need to hold on to him until another forward comes in.