Manuel Pellegrini has already been extremely active during this summer's transfer market, bringing in a whole host of new signings, but the Chilean is still lacking a top class target man to spearhead his attack.
West Ham do have Andy Carroll, of course, but the big Geordie is far from reliable from a fitness perspective, and the addition of an established striker at the London Stadium might just be the final piece of the puzzle for Pellegrini.
Tottenham signed Llorente from Swansea City in the summer of 2017, for a fee believed to be worth in the region of £12 million, but he has so far failed to establish himself in north London, scoring just five goals in 31 appearances in all competitions.
That isn't to say that the 33-year-old doesn't still have a lot offer at the very highest level, though.
Llorente has enjoyed wonderfully successful spells at Athletic Bilbao, Juventus and Swansea City, and if he is given regular game-time at West Ham, he would surely prove to be a useful asset for Pellegrini's side.
The Spaniard excels in linking play between the midfield and attack, and with some of the wonderful footballers that the Hammers have in the midfield department, his talents would really come to the fore in east London.
The Daily Mail claims that Tottenham are looking for around £7 million for the striker, and in today's day and age, that would represent decent value for money for West Ham.