The 33-year-old is currently Spurs second choice striker, serving as back-up to Harry Kane.
He arrived at Spurs during the summer of 2017 from Swansea City but has struggled to make a significant impact while donning the jersey of the Lilywhites.
It looks highly unlikely that Spurs will want to keep Llorente when his current contract with the club expires at the end of the season.
The player is also approaching the end of his career so he will surely want to play as regularly as possible.
The prospect of returning to his homeland is also something that will appeal to him at this stage.
“I’ve been away from home for many years, I’d love to go back to the Spanish league,” the veteran told Sport.
“I came in and things went well, so I’m happy to have helped the team.
“I hope I continue to have opportunities, it’s important for me because it gives me the confidence to keep working, it’s not easy when you do not play because mentally you have to be very strong to continue training hard.”