Lloris has played 361 Premier League games for Spurs over 11 years since he signed from Lyon for £11m in 2012.
However the former France international lost both his spot as Spurs' no.1 goalkeeper and the captain's armband ahead of this season.
Summer signing Guglielmo Vicario and Fraser Forster are now first and second choice respectively under new manager Ange Postecoglou, whilst Heung-min Son has been appointed skipper.
Now, Lloris is in talks with Los Angeles FC - the club that Gareth Bale retired at.
His current deal with Spurs expires in June 2024.
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Lloris hasn't played any minutes for the north London outfit this term. He stated in the summer that he wanted to move on to another club, but no deal materialised.
He also retired from international football at the start of the year.
The goalkeeper, who turned 37 on Boxing Day, had been a hit at Spurs.
He's made 444 appearances for the club, including the 2019 Champions League final defeat to Liverpool.
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He won the 2018 World Cup with France and played in the 2022 World Cup final loss against Argentina during his time at Spurs, too.
Discussing the goalkeeper's future recently, Postecoglou said: "[His future] is not my decision. It's a decision for Hugo and the club. I don't have that power and don't want that power.
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"Hugo is a member of this squad and how he trains every day is important to me. If he wasn't then I'd be dealing with it but I haven't had to, he has been absolutely first-class.
"As a manager, I don't take that for granted because that could be a problem for me. For most managers, it is the ones who aren't playing who give you the biggest headaches. It's his decision to make."