The 22-year-old was a key figure for Ajax in their Champions League campaign last season and has therefore attracted attention from all over Europe.
Ole Gunnar Solskjaer is hopeful that they can capitalise on Ajax's failure to qualify for the Champions League knockout stages this year.
Ajax are now open to offers for Donny van de Beek as Solskjaer is desperate for reinforcements in the January window. United are keen to continue their policy of signing younger players to help grow and develop, and Van de Beek meets the criteria.
United are desperately short of options in central midfield with Paul Pogba and Scott McTominay both sidelined. Andreas Pereira and Fred started against Manchester City on Tuesday night but were given the runaround before Nemanja Matic was introduced.