Diego Costa's clash with Antonio Conte – coupled with Michy Batshuayi's struggles – meant a move to Stamford Bridge was likely.
Conte managed Llorente at Juventus and was keen on a Premier League reunion.
However, the 31-year-old has revealed Swansea blocked a move to Chelsea and his sole focus is keeping Paul Clement's side in the top flight.
Fernando Llorente saw a move to Chelsea break down
Fernando Llorente played under Antonio Conte at Juventus
Chelsea stars meet Will Ferrell after beating Arsenal
Sat, February 4, 2017
Chelsea stars met Will Ferrell after beating Arsenal at Stamford Bridge
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Will Ferrell poses with Marcos Alonso and Pedro
"I already know Conte from Juventus," Llorente told Spanish publication Marca.
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"But it's difficult in the winter when there's a way out from a side you're playing for and it's normal that they didn't go ahead with the deal.
"I'm very focused on the team and am looking forward to helping save us from relegation.
"The last few games I've been happy with as we've gotten away from the bottom.
Diego Costa has since made up with Antonio Conte
"It will be a very tough fight, though, and we hope to get further ahead when we face Leicester in a final next Sunday."
Swansea go up against Leicester aiming to inflict more misery on Claudio Ranieri's struggling champions.
The Foxes lost 3-0 to Manchester United yesterday and now sit just a point above the relegation zone.