Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The Spain international has been pushing for a move since the summer, with it his desire to take on a new challenge after spending his entire professional career to date with Bilbao.
He feels that he has given loyal service to the club, making over 300 appearances and netting over 100 goals.
A switch to the Premier League has been widely touted, with the likes of Arsenal, Liverpool and Manchester United said to be keen.
Llorente has been restricted to a bit-part role at Bilbao this season after conceding that he wants to move on, but the Primera Liga outfit are reluctant to sell and have no intention of discussing a deal during the winter transfer window.
"This player makes our team more competitive and his future will be decided by the club," said Bilbao president Josu Urrutia.
"At the moment we need to maintain the quality level within our squad, not reduce it.
"Llorente will stay with us until the end of the season."