Gazzaniga, 26, has impressed in between the sticks when given the chance by Mauricio Pochettino, starring against PSV Eindhoven in the Champions League. He even won his first Argentina cap on Tuesday night against Mexico.
Question marks have been raised over the performances of Lloris of late, but he has since started Spurs' last five Premier League outings - keeping three clean sheets in that time.
Former Spurs and Chelsea goalkeeper Sullivan reckons Lloris will retain his place in the side ahead of Saturday's Premier League clash between the two sides.
"The manager obviously knows the qualities of the two goalkeepers," Sullivan said. "I just saw the highlights of France V Holland, and Lloris was fantastic. He played really well and kept the score down to just 2-0.
"He's still in good form and at top clubs, that's what you want. I think Lloris is still going to be the number one choice at Spurs. Looking at the game against Holland, he still looks fantastic."
Lloris' campaign so far has been affected by injuries, suspension and indeed the drink-driving charge, but he remains Spurs captain and after winning the World Cup in the summer with France, he is likely to remain in goal.
A win for Spurs would see them leapfrog Chelsea into third place, with Maurizio Sarri's side currently sitting in third. Liverpool and Manchester City remain in the top two, having yet to lose a league game.
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