Spurs boss Andre Villas-Boas is ready to make a move to bring Llorente to White Hart Lane before the transfer window closes on Friday.
Villas-Boas has money to spend on new players, following the sale of Luka Modric to Real Madrid.
Llorente has long been linked with a move away from Bilbao.
Juventus, Manchester United and Arsenal are among the club’s who are reported to be interested in the striker.