The 23-year-old has been strongly linked with a move to the Premier League in recent months, with Nice said to be willing to part ways with the centre-back in 2024.
Spurs are believed to be the latest English top-flight clubs to join the likes of Manchester United, Liverpool and Chelsea in the race to sign the highly-rated Frenchman.
Ange Postecoglou's side are currently light in the centre-back department and the club are understood to be prioritising defensive reinforcements in the New Year.
Summer signing Micky van de Ven made an impressive start to life at Tottenham, but he is currently sidelined with a hamstring injury, leaving Postecoglou with Cristian Romero, Eric Dier and 18-year-old Ashley Phillips as his remaining three centre-back options.
While Phillips is considered as a player for the future, Dier is facing an uncertain future at Tottenham, with his contract due to expire in June 2024.
Dier has fallen down the pecking order in North London since the arrival of Postecoglou, who has preferred to play full-backs Ben Davies and Emerson Royal in central defence over the Englishman in recent weeks.
Spurs have been linked with a number of centre-backs ahead of the January transfer window, but Todibo is believed to be one of their leading targets.
According to the Daily Mail, Todibo's representatives held further talks with Tottenham chiefs last week to discover whether the £35m-rated defender would be interested in a move to North London.
The report adds that Todibo is keen to join Postecoglou's rejuvenated squad during the winter transfer window, seemingly putting Spurs at the front of the queue for his signature.
Todibo has spent nearly three years at Nice and has developed into a key player for the Ligue 1 club, making 117 appearances across all tournaments.
The former Barcelona defender has been a standout performer in the Nice side that currently sits second in the French top-flight table, helping Les Aiglons keep nine clean sheets in the process.
As well as Todibo, who still has four years remaining on his contract with Nice, Spurs are also said to be keeping tabs on Club America's Sebastian Caceres, Everton's Jarrad Branthwaite, Crystal Palace's Marc Guehi and Bournemouth's Lloyd Kelly ahead of the New Year.
Postecoglou is believed to be targeting at least three new signings in January, with the Australian keen to bolster his squad with a new midfielder and forward as well as a central defender.