The 22-year-old, who is currently on World Cup duty with the Netherlands, reportedly agreed to join the Red Devils for a fee in the region of £8m.
However, agent Carl Thomas denies these claims, saying in quotes attributed to the Express: "We have no agreement with Manchester United, nor have we signed for them.
"I don't know where this rumour came from. Stefan is concentrated only on the World Cup and he wants to continue doing well."
De Vrij has spent his entire career at Eredivise outfit Feyenoord after progressing through their youth academy.