This news is set to attract the attention of Chelsea and Manchester City, who are both reported admirers of the Spaniard.
Llorente has spent his entire career at the Basque club and after a fantastic season last time out, is set to want more than what is being offered to him in terms of wages.
He has less than 12 months left on his contract and Bilbao could of course run the risk of losing him on a free next summer.
It is being suggested that it would take around £15 million to secure his services and this could spark a bidding war between the two English Premier League teams.
Llorente is certainly a talent and may feel as though it is time to make a move to a side that will be playing in the Champions League next season as at 27-years-old, he is in his best playing days.
It is sure to be a deal that many people keep an eye on and a few more clubs across Europe may make a move for the Spanish international.