Llorente has been heavily linked with a move to Chelsea throughout the summer, but the Blues are yet to agree a fee with Swansea.
And it looks as though the Premier League champions could miss out after Swansea accepted an offer from Tottenham, believed to be worth £15million.
Chelsea are expected to return with another bid to land the Spain international before tonight’s deadline.
BBC Sport reporter David Ornstein tweeted: “#THFC shock Llorente offer accepted #SwansFC – Chelsea close for weeks but no bid accepted.
“#CFC set to counter, outcome too close to call.”
And should Tottenham sign Llorente, it could see Vincent Janssen leave the north London outfit.
The Holland international arrived at Spurs last summer but failed to find his feet in England, scoring just two Premier League goals in his 28 Premier League outings.
“If Llorent joins Spurs (they’re in pole but he’s torn & no #CFC deal yet) it’s possible Janssen to leave #THFC on loan before window shuts.”