The 27-year-old, who is an established member of the Spanish squad, is out of contract next summer and could then move for nothing so there are a host of clubs thinking about making a move with Liverpool said to be very keen.
Bilbao do not want him to leave so they maybe prepared to sell him in the new year rather than see him walk away for nothing but the Reds are only one of many interested parties.
Under the Bosman ruling, Llorente will be allowed to talk to clubs in January and sign a pre-contract agreement ahead of a move next summer and there will be no shortage of interest.
As well as Liverpool boss Brendan Rodgers, Spurs and Chelsea have also been linked, while Serie A champions Juventus are poised to offer Llorente terms.
Liverpool last week