The 30-year-old has emerged as a target to solve United's longstanding issues in the middle of the park, with the protracted pursuit of Frenkie de Jong no closer to completion.
Talks with Madrid for Casemiro are advancing after United negotiators visited the Spanish captial earlier this week, with a deal worth in the region of £60m mooted.
The Brazil international has three years remaining on his contract at the Bernabeu and has played an integral role in winning five Champions League and three La Liga titles since joining in 2013.
Casemiro's starting status has come under threat, however, following the €80m signing of Aurelin Tchouameni from Monaco this summer.
Tchouameni started Madrid's first La Liga game of the new campaign against Almeria, with Casemiro only appearing as an 83rd-minute substitute for Carlo Ancelotti's side.
Erik ten Hag is eager to add to his squad after a miserable start to life at Old Trafford, losing both of his first Premier League games in charge to leave United bottom of the table.
While left-back Tyrell Malacia, playmaker Christian Eriksen and centre-half Lisandro Martinez have all arrived, United have been frustrated in efforts to add primary target De Jong and others.
United are understood to still be in the market for a forward, with the possibility of a loan for Chelsea winger Christian Pulisic explored. A back-up goalkeeper and right-back are also being considered.