The Sunday Mirror claims Blanc is ahead of Jose Mourinho and Carlos Queiroz for the job.
Fergie will reportedly remain in charge at Old Trafford until at least the end of next season.
Blanc spent two years at Old Trafford before he ended his playing career and Fergie has several times tried to bring him in to work alongside him at United.
A United insider told The Sunday Mirror: “Replacing Sir Alex will be the toughest job since Matt Busby left the club.
“It isn’t just about winning at United. It’s about playing the game the right way and upholding the traditions.
“There is a lot of admiration at Old Trafford for the job Blanc has done at Bordeaux and the style of play he has imposed.
“It is no secret at the club that he became close to Sir Alex when he was a United player. There is still a lot of mutual respect.”
