The 36-year-old France international joined Spurs in 2012 from Lyon and has featured 447 games for the north London outfit.
Lloris has one more year left on his contract with Tottenham and he has been tipped to head elsewhere this summer.
It is suggested that several European outfits are interested in Lloris and Lazio are particularly keen on acquiring his services.
And, according to French radio station RMC, the interest between Lloris and Lazio is mutual.
Lloris is currently negotiating a contract with the Italian club and Tottenham are claimed to be set to release him on a free transfer due to his service to the club.
It has also been suggested that the Spurs star was offered to Real Madrid as an alternative to the injured Thibaut Courtois.
Now it remains to be seen whether the Italian club will be able to agree a deal with Lloris and take him to Serie A this summer.
