New manager Andre Villas-Boas has decided he wants to sign a new goalkeeper, despite the fact he has Brad Friedel, Heurelho Gomes and Carlo Cudicini already at the club.
Spurs officials have been locked in discussions with Lyon over a summer move, with the French club wanting in the region of £16million to part with the 25-year-old.
The Portuguese manager views Lloris - who captained France during Euro 2012 - as the man he wants to be his new first-choice goalkeeper.
Spurs have been encouraged to hear that Lloris would give serious consideration to a move to White Hart Lane should the clubs agree a fee.
Villas-Boas is keen to have the shot-stopper on board by the time Spurs fly out for their pre-season tour of USA, which kicks off against LA Galaxy on July 24.