The Red Devils are increasingly confident they will be able to sign the Brazil international for £60m, per Goal.
A deal for Adrien Rabiot also fell through this week, leaving Casemiro as United's main midfield target.
The move was originally considered a long shot by the United hierarchy.
However, Casemiro is reportedly keen on a move after Real's signing of Aurelien Tchouameni this summer.
The 30-year-old is now weighing up whether the enticement of a new challenge outweighs the lack of Champions League football at Old Trafford.