According to Spanish news outlet Don Balon who say the Swansea star’s agent has contacted Zinedine Zidane.
However, the Frenchman has snubbed the chance to secure his signature.
Don Balon say Zidane is happy with his current crop of strikers.
It’s suggested he’s keen to persevere with Borja Mayoral as a back-up option.
If Don Balon’s report is correct, the news could be a huge relief to Antonio Conte.
The Italian is working hard trying to complete a number of deals before next Thursday’s transfer deadline – and Llorente has emerged as a top target.
He played under Conte at Juventus and Chelsea tried to lure him to Stamford Bridge in January.
That potential move failed to come off but the Blues are reportedly now set to renew their efforts at landing him.
The Telegraph claim Chelsea are set to offer £15m for the 32-year-old.
It is said Llorente is interested in working with Conte again and is well aware of the interest coming from west London.
Swansea are reportedly closing in on a deal to bring Manchester City outcast Wilfried Bony back to the club.
Bony was sold to City in 2015 but has struggled at the Etihad