Spurs announced that the veteran goalkeeper will stay behind to explore potential transfer opportunities.
Lloris has reached the end of his Tottenham career, with the club eager to move him on after 11 years of service.
They have already signed Guglielmo Vicario from Empoli for around £17 million to replace the Frenchman.
Lloris has made 447 appearances for Tottenham, keeping 151 clean sheets in that time.
He arrived from Lyon in 2012 and has established himself as one of the best keepers in the world.
During his time with Spurs, he went to the 2018 World Cup with France and lifted the trophy. They also won the 2020/21 Nations League title.
Lloris and Les Bleus reached the 2022 World Cup final but ultimately lost to Argentina. The goalkeeper subsequently retired from international duty to focus on his club career.
He had a poor season for Spurs, making several high-profile mistakes and looking far from his best.
The Nice-born keeper has offers from clubs in France and the Saudi Pro League.
He is also of interest to Serie A giants Inter Milan but has not decided on the next step in his career.
Harry Kane is part of Tottenham’s touring squad despite speculation linking him with a move away from the squad.
Kane has been strongly linked with Bayern Munich, but the Bundesliga club are reluctant to meet Tottenham’s asking price.
Despite having just one year left on his contract, Tottenham are demanding a fee of over £100m.
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