The Red Devils are yet to make an announcement on their managerial situation, but it is understood that Ralf Rangnick will become the new boss for the remainder of the 2021-22 campaign before taking on a consultancy role with the 20-time English champions.
Following Sunday's 1-1 draw with Chelsea in the Premier League, Bailly was asked about the situation, and the Ivory Coast international said that the players had been informed "about the arrival of the new manager".
"Yes, we've been told in the dressing room about the arrival of the new manager," Bailly, who played the full 90 minutes at Stamford Bridge, told RMC Sport.
Rangnick could be in charge for Thursday's Premier League clash with Arsenal providing that he manages to secure his work permit paperwork in time.
The 63-year-old, who has been working with Lokomotiv Moscow as head of sports and development, last managed RB Leipzig in 2019.