Luis Suarez refused to rule out a return to Liverpool and insists he will never play for another Premier League club.
Radamel Falcao has played down talk of a summer move to Juventus and says he is fully focused on Manchester United.
Cudicini moved to White Hart Lane in January 2009 on a free transfer after spending nine years with London rivals Chelsea.
But the 39-year-old was restricted to just 20 appearances for Spurs because of injury - including a motorcycle crash with resulted in two fractured wrists and some pelvis damage.
The Italian stopper has fallen further down the pecking order at Tottenham and has an opportunity for some regular game time in the States.
Should the move go ahead, Cudicini will join former Tottenham striker Robbie Keane at the Galaxy.