The last several days have seen progress in the negotiations to sign the 24-year-old Argentine.
Martinez, linked with Arsenal, is reportedly willing to change teams.
Martinez, who joined the team on a four-year agreement from Feyenoord, may mark the club’s second acquisition under new manager Erik ten Hag.
Christian Eriksen has not yet officially signed his contract, according to United.
The centre defender joined Dutch club Ajax in 2019 and has played 120 times since then. He has made seven appearances for Argentina.