Blind, 24, is yet to agree personal terms and undergo a medical, but United are hopeful the versatile player will complete his move to Old Trafford before the transfer window shuts on Monday night.
Reports in Holland suggest the agreed fee is 18 million euros (£14.2million).
Blind was part of Louis van Gaal's World Cup squad and is the son of former Holland defender Danny Blind.
The Ajax youth academy product can play in a variety of positions, including left-back and in central midfield.
If Blind complete his move to Old Trafford, he will become the club's fifth summer signing.
Van Gaal has already signed Angel Di Maria, Luke Shaw, Ander Herrera and Marcos Rojo for a total of around £133million.
After watching his team draw against Sunderland and suffer defeats to Swansea and MK Dons, Van Gaal thinks his squad is in need of an overhaul.
The 20-time English champions have been linked with a move for Arturo Vidal, but are understood to be cautious about bidding for the Juventus midfielder due to his knee injury.
Another target is Roma's Kevin Strootman, but he again is also just coming back from injury.
Van Gaal is expected to sell a number of fringe players before Monday night.
Tom Cleverley is in talks with Aston Villa, Shinji Kagawa has been linked with Valencia and Javier Hernandez is a reported target for Juventus.
Van Gaal will be looking to finally record his first competitive win as United boss at Burnley on Saturday afternoon.
Source : PA
Source: PA