According to the Daily Mail, the Red Devils are eager to sign the Argentina international ahead of Premier League rivals Arsenal.
The same article states that Manchester United have increased their offer from £38m to £43m to almost meet Ajax’s asking price for the 24-year-old.
According to the same story, Argentine defender Martinez has already requested that Ajax allow him to leave the Amsterdam club in the summer transfer window.
The Daily Mail goes on to reveal that Arsenal and Manchester United initially both launched identical £38.5m offers for the South American defender.
The media outlet explains that Manchester United have now increased their offer by £5m because Erik ten Hag is eager to wrap up a deal for a player that he knows extremely well.
The 20-time English champions are hoping their increased bid will help Manchester United to usurp Arsenal in the race to sign the South American defender.
Martinez made 23 top-flight appearances under Ten Hag at Ajax last season to help the Dutch club win the Eredivisie title for the second successive season.
The 5ft 9ins center-half has been capped seven times by Argentina over the past four years since making his debut in 2019.