Llorente left Swansea for Premier League rivals Tottenham Hotspur in the summer for a transfer fee reported by The Times to be worth £11.5m.
According to the report, Chelsea manager Antonio Conte wanted to sign the Spain international striker in January 2017.
Llorente worked with Conte at Italian and European giants Juventus and is a proven goalscorer.
The 32-year-old former Athletic Bilbao and Sevilla striker scored 15 goals and provided one assist in 28 Premier League starts for Swansea during the 2016-17 campaign.
The Spaniard, though, has yet to start a league fixture for Spurs this season, with England international striker Harry Kane the clear first-choice player upfront for the North London outfit.