The French outfit are enjoying a strong campaign, currently sitting second in the Ligue 1 table, while they are in the last-16 stage of the Coupe de France.
Todibo and Thuram are among the team's most-discussed players, with Liverpool thought to be interested in the latter, while Man United continue to be linked with the former.
There had even been suggestions that a move to Old Trafford could take place during the January market, but Nice's sporting director has ruled out a mid-season departure.
"As we've said since the offset, we are working on stability, and stability is keeping your best players," 90min quotes Ghisolfi as saying.
"Jean-Clair and Thuram are definitely that, as players and as leaders as they are vice-captains. We absolutely want to keep them."
The 24-year-old was strongly linked with a move to Old Trafford during last summer's transfer window, but it is understood that a deal would only have been possible if Harry Maguire had moved on.
A recent report claimed that Man United are still keen on the defender, who is valued by his club in the region of £52m.
Chelsea have also been credited with an interest in the Frenchman, with the Blues expected to be in the market for a replacement for Thiago Silva at the end of the campaign.
Todibo has featured on 118 occasions for Nice in all competitions, scoring twice and registering one assist in the process, completing a permanent move to the club in the summer of 2021.
The centre-back started his professional career with Toulouse, making 10 appearances for their first team, before Barcelona brought him to Camp Nou in 2019.
Todibo found it difficult to make his mark for the Catalan side, though, featuring on just five occasions, and he left in 2021 after three loan spells away from the club.
The defender was capped on two occasions by France towards the end of last year and is battling to be in their squad for this summer's European Championship.
Man United could overhaul their defence this summer, with arguably Lisandro Martinez the only current first-team centre-back guaranteed to be at the club next season.