Llorente has been at Tottenham since 2017, but he is currently a free agent.
Spurs were not happy to keep Llorente at White Hart Lane on his previous wage, as he was on a contract worth £100,000-a-week.
However, Spurs have now offered Llorente a chance to return on reduced terms.
Whether the World Cup winning Spaniard will accept that offer remains to be seen.
However, Llorente may still feel that he has work to do at Tottenham, as his initial target was to help them win the Premier League.
"I'm very very happy to join Tottenham, it's an amazing club and all I say is that I've come here to help Tottenham to win the title,” Llorente said to the Daily Mirror after signing for Spurs for the first time.
If Llorente does stay at Tottenham it should help add depth to Mauricio Pochettino’s squad up-front.
Llorente did a good job covering for Harry Kane last term, and scored some crucial goals for Tottenham in their run to the Champions League final.
The 34-year-old striker does have options from other clubs though, so whether he will return to White Hart Lane remains to be seen.
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