The Red Devils have already made a significant impression in the transfer window, having recruited Andre Onana, Mason Mount and Rasmus Hojlund.
They are still determined to make further additions, with Erik ten Hag keen to strengthen in defence and the centre of midfield.
With Harry Maguire believed to be close to joining West Ham United, the Red Devils have started searching for a new central defender.
They have seemingly been impressed by Todibo, who has emerged as a credible candidate to replace Maguire in the Man United squad.
Nice boss Francesco Farioli is keen to keep hold of the 23-year-old, but he was unable to offer any guarantees over his future.
Farioli was speaking in a press conference ahead of Nice's 1-1 draw with Lille in the first game of the new Ligue 1 season.
According to journalist Fabrizio Romano, Man United sent a scout to watch Todibo play the full duration of Friday's contest.
Todibo and his teammates were unable to stop Lille's Bafode Diakhite from equalising in stoppage time after Gaetan Laborde had opened the scoring in the first half.
The 23-year-old joined Nice on an initial loan deal from Barcelona in February 2021, before making the move permanent in the following summer.
During his two-year stay with the club, the centre-back has made a total of 104 competitive appearances and has chipped in with two goals.
While Todibo is seemingly under consideration, it remains to be seen whether a potential deal depends on Man United's pursuit of Bayern Munich defender Benjamin Pavard.
A recent report indicated that the Red Devils are in pole position to sign the France international, who has entered the final 12 months of his Bayern contract.
The German champions will reportedly sanction a sale if Man United meet their €30m (£25.97m) asking price for the 27-year-old.
Ten Hag's side will begin their Premier League campaign on Monday when they welcome Wolverhampton Wanderers to Old Trafford.