It is not just the three Premier League giants that want to sign the 24-year-old, Eintracht Frankfurt, Atletico Madrid and Sevilla are also reported to be keen.
Chelsea, of course, faces a two-match transfer ban and will have to drop out of the running if they fail in their final appeal to the Court of Arbitration for Sport and the player has already stated that he would rather his next club be outside of Spain, which rules out Atletico and Sevilla.
That leaves just Man Utd, Arsenal and Eintracht Frankfurt and you can probably narrow it down further with United not being able to offer Champions League football next season, though in all fairness that does not mean that Llorente will not sign for them.
Arsenal has financial restrictions and Eintracht Frankfurt are not exactly a marquee club.
So no one club can be seen as a front runner right now but if one has to hazard a guess Arsenal would seem a logical destination if they qualify for next seasons Champions League and in turn get an enhanced transfer budget.
Real Madrid may prefer to loan the player out but that is probably unlikely as they will need to raise funds if they are to undertake the sort of spending spree that they will need to do in order to rebuild their team.