Old Trafford executive vice-chairman Ed Woodward has held meetings with the AC Milan midfielder's representatives, with the Dutchman keen to work under Louis van Gaal again.
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Having already brought Ander Herrera to the club this summer, manager Louis van Gaal made it clear to United officials that he is happy to work with what he has in the midfield area - at least until his top target, Kevin Strootman, fully recovers from a serious knee injury.
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But executive vice-chairman Ed Woodward has been working tirelessly behind the scenes in a bid to strengthen the Dutchman's options - and having identified De Jong as a potential recruit, met with the Milan midfielder's representatives in London on Tuesday.
Those talks are understood to have gone well, with De Jong desperate to link up with Van Gaal.
The Dutchman could now become United's third major summer signing, following on from the arrivals of Herrera and Luke Shaw.
Van Gaal is understood to have given the move the green light, having worked well with De Jong in his former role as Netherlands coach and in particular at this summer's World Cup.
The 29-year-old was forced out of the second round victory over Mexico early on with a groin problem, but made a remarkable return from injury for the semifinal defeat to Argentina and was singled out for praise by Van Gaal for his contribution during the group stages.
"I don't like singling out players, but Nigel de Jong was inspirational," Van Gaal said after the 3-2 victory over Australia.
United's move for De Jong comes on the back of a prolonged and so far unsuccessful pursuit of Juventus midfielder Arturo Vidal.
Despite the player and Juventus both going on record to insist a deal with United would not happen, reports of a move persist.
The arrival of De Jong, however, would appear to put those links to bed - if a deal can now be successfully concluded with Milan.