The Daily Express says MLS clubs are queuing up to make him a money-spinning offer to join Thierry Henry in America.
Gallas has been a revelation at White Hart Lane in recent weeks. Having been given the captaincy, he has inspired Spurs to victories over former club Arsenal and Liverpool and helped them qualify for the last 16 of the Champions League.
Manager Harry Redknapp has already described free-transfer Gallas as one of the signings of the season and is keen to take advantage of the option of a further year on the initial 12-month deal he signed.
But New York Red Bulls made Gallas an offer in the summer and other MLS clubs have been alerted to his good form and the fact he could become available if Spurs do not act quickly to tie him down to another year.