Spurs were heavily linked with a move for the France number one, who would provide competition for veteran stopper Brad Friedel and ultimately succeed the ageing American between the posts at White Hart Lane.
However, Spurs' offer was not deemed acceptable, but Lyon chairman Jean-Michel Aulas has admitted that Lloris could still leave the club.
Michel-Aulas said: "Hugo wants to play in one of the best clubs in Europe. This year there was an approach from Tottenham that was quickly rejected.
"If he absolutely wants to leave, we will look at the proposals but they must be consistent with what we want. If not, he will stay."
Lloris was the French captain at Euro 2012, where they reached the quarter-finals.