Blues head coach Antonio Conte has been keen on a reunion with Llorente - who worked with him at Juventus - since January, but so far, the Italian has failed to tempt the Welsh outfit into a sale.
However, according to The Telegraph, Chelsea are ready to launch another approach for the 32-year-old, who has less than a year remaining on his contract at the Liberty Stadium.
It has been claimed that the Premier League champions will offer a fee of £15m for the Spanish international, who is yet to feature this season because of a fractured arm.
Last season, Llorente netted 15 goals in the top flight, with his contribution proving decisive as Paul Clement's team avoided relegation to the Championship.
If a move for Llorente is successful, it would leave Chelsea with three strikers on their book, unless Michy Batshuayi is allowed to leave the club on loan.