The Red Devils made a formal offer for the versatile 24-year-old defender on Saturday but, according to De Telegraaf, the Dutch giants are set to knock back that approach.
United are said to have offered €41 million with an additional €4m in bonuses but Ajax are holding out for closer to €50m.
Mikel Arteta wants to sign Martinez to act as cover for Gabriel Magalhaes and left-back Kieran Tierney who missed the run-in last season due to a serious knee injury.
Martinez, however, is said to prefer a move to Old Trafford where he would link up against with his former manager Erik ten Hag.
Ten Hag has been forced to wait patiently to make additions to the squad he inherited from Ralf Rangnick.
United are hopeful of making significant progress in the next 10 days with finaling a move for Frenkie de Jong a priority.
The Red Devils also expect to confirm the signing of left-back Tyrell Malacia in the next 48 hours after they overcame a late complication.
Ten Hag is also keen to raid his former club for Brazil international winger Antony, while United are also waiting on Christian Eriksen’s decision over his future.
The Denmark international is considering a rival offer from Brentford, but his former club Tottenham have cooled their interest.
MORE : Chelsea ready to pounce for Frenkie de Jong if Manchester United move falls through
MORE : Manchester United’s Tahith Chong in talks to return to Feyenoord
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