Llorente has earned a reputation as one of Spain's leading strikers in his seven season as San Mames, but has so far stayed loyal to Bilbao by spurning the advances of Europe's biggest sides.
Real Madrid have regularly been linked with the towering striker over the last year, while Bayern were also rumoured to be interested.
And while the summer transfer window passed without much drama involving Llorente, Cadena Ser reports that Bayern could be ready to reignite their interest in the Spain international in January.
One factor that could finally see Llorente prepared to leave Bilbao has been the appointment of Marcelo Bielsa to replace Joaquin Caparros at the helm of the club, a decision that has reportedly unsettled the 26-year-old striker.
Llorente has scored 83 goals in 240 appearances for Bilbao.