The North London outfit are in contention to clinch the Europa League trophy if they secure a quarter-final spot from tomorrow night's second leg against Inter Milan.
If successful, Gallas believes that Spurs are capable of eclipsing arch rivals Arsenal and West London opponents Chelsea as the capital's elite club.
"Tottenham can be the biggest club but for that they have to win some trophies and then they will start to be the biggest club in London," the London Evening Standard quotes Gallas as saying.
"We have to win some trophies, and then I think people will start to respect Tottenham more. The fans will be more proud to walk with their shirts on their backs but we need to lift trophies. It is as simple as that."
Spurs are currently above Arsenal and Chelsea in third place in the Premier League table.