The Swansea City striker, 32, will be back up for lead striker Harry Kane as Mauricio Pochettino's side heap more transfer misery on Antonio Conte after the Blues lost out on Alex Oxlade-Chamberlain less than 24 hours ago.
Spurs were first to make an offer for Llorente with Chelsea following soon after. Llorente has completed a medical with Spurs but Vincent Janssen has been requested on loan by the Swans as part of the deal.
The deal is yet to be fully completed and Chelsea remain hopeful, but Llorente has gone through much of the process to move to North London, having been offered a more prominent role under Pochettino.
Chelsea still have Alvaro Morata and Michy Batshuayi on their books, with Diego Costa's move to Atletico Madrid still a possibility due to the Spanish window closing on Friday instead of Thursday.