United have been heavily linked with the 24-year-old Spain international as they look to add attacking reinforcements to cover the loss of last season's top scorer Zlatan Ibrahimovic.
Morata's agent, Juanma Lopez, revealed that free-spending AC Milan have also shown an interest in the former Juventus hitman but says Madrid have rejected an "unsatisfactory" offer from the Italian side.
"It's a club with a lot charm, a very interesting option," Lopez told Calciomercato of United.
"I can say that there's a very important offer and the decision now rests with Real.
"I cannot tell (if an agreement is close), we'll see."
Regarding Milan's interest, Lopez added: "I can confirm there had been regular contact until a few days ago. Quite simply, Real Madrid considered the offer from the Rossoneri unsatisfactory."
Sky in Italy reported last Tuesday night that United had seen a £52.4m offer rejected by the Champions League and La Liga winners, with Real thought to want in the region of £78m for the forward.