The centre-back's future is currently the subject of much speculation, with Manchester United believed to view the Frenchman as the ideal replacement for Harry Maguire.
The Red Devils have allegedly agreed a £30m deal with West Ham United to sell Maguire, with the defender's time at Old Trafford set to come to an end.
Todibo has another four years left to run on his contract, and Farioli has expressed a desire to keep hold of the 23-year-old, along with midfielder Khephren Thuram, who has been linked with Liverpool.
However, the new Nice boss could not guarantee that Todibo would stay at the club this summer.
"I also have two vice-captains Khephren Thuram and Jean-Clair Todibo who are among the best players in the team," France Bleu quotes the manager as saying at a press conference.
"We would like both players to stay until the end of the season. But the reality of the transfer window escapes me. We'll see what happens. As long as they're here, I'm enjoying having them."
Meanwhile, Nice captain Dante added: "Of course we would like Todibo to stay. But it can be complicated. We have to wait to see who will want to buy him and if everyone finds himself there.
"He is a leader, a very strong player mentally, he has improved a lot and he is ready to reach the very top level."
Man United have already boosted their squad with the signings of Mason Mount, Andre Onana and Rasmus Hojlund during this summer's transfer window.
However, there are expected to be at least two more incomings before September 1, with a new centre-back being signed to replace Maguire, in addition to a defensive midfielder.
Fiorentina's Sofyan Amrabat is thought to be the favourite to arrive at Old Trafford this month.
There will be midfield exits during the current market, meanwhile, with Fred said to be closing in on a switch to Fenerbahce, and Donny van de Beek in advanced talks over a move to Real Sociedad.
Scott McTominay is also still being linked with a move to West Ham, although it remains to be seen whether Ten Hag is prepared to let three senior midfielders leave in the coming weeks.