Llorente played third-fiddle for the Old Lady last season, with Alvaro Morata and Carlos Tevez seen as Massimiliano Allegri's key men in attack, and the recent acquisitions of Paulo Dybala and Mario Mandzukic appear to have confirmed the Spaniard's fate.
The player's brother and agent, Jesus, recently told Portuguese paper O Jogo: "Fernando wants to be playing regularly so that he doesn't lose his place in the Spain national team. Nothing can be excluded."
It has not been the most fruitful of spells for Llorente since leaving Athletic Bilbao for the Serie A champions. Despite playing well for Juventus, he has never quite been able to push on to the next level during his time in Turin.
The Spaniard, who has scored seven goals in 23 international appearances, is strong in the air and can play as a traditional number nine, or in a front-two pairing, which makes him a suitable target for either Tottenham or West Ham.
Amid speculation in the Daily Mail linking the Hammers' Diafra Sakho with an exit, Llorente could find playing time easier to come by at Upton Park. Whereas at Spurs, he would be forced to compete for first-team royalties with Harry Kane, who produced the form of his life last season.