The Dutchman – who starred for Louis van Gaal at the World Cup – was believed to be a top target for the Red Devils ahead of the coming season as their new boss steps up his plans to replace Nemanja Vidic and Rio Ferdinand.
The Rotterdam club are thought to be resigned to losing their man, but United will not be the club he’s heading to.
Lazio are instead leading the race, and it is thought that the enforcer is keen to move to Italy.
LVG is instead looking at Thomas Vermaelen, and may also step up a move for de Vrij’s international and club team-mate Bruno Martins Indi or German World Cup winner Mats Hummels.
United are set to adopt van Gaal’s successful 3-4-1-2 formation next season, but, as it stands, they only possess Phil Jones, Chris Smalling and Jonny Evans as orthodox options at the back.