Everton are reportedly also monitoring Llorente’s situation, with Ronald Koeman keen to sign a targetman to replace Romelu Lukaku, but the London clubs are favourites.
As with Chelsea, Mauricio Pochettino’s side can offer Champions League football, which could sway Llorente’s final decision.
Elsewhere, despite sealing the signings of Paulo Gazzaniga, Davinson Sanchez and Juan Foyth, Spurs remain keen to add to their squad ahead of the transfer deadline, with a midfielder firmly on the agenda.
Everton’s Ross Barkley is a long-term target, while The Telegraph report that Tottenham could go head-to-head with West Ham United to sign Andre Gomes on loan from Barcelona.
Spurs expressed an interest in the Portuguese international earlier this week, but face late competition from West Ham after they failed to agree a deal for William Carvalho.