Representatives for Alvaro Morata met with Real Madrid on Monday morning to discuss the striker's future.
Manchester United want to sign the Spanish international to replace Zlatan Ibrahimovic and the player is understood to be keen on a move to the Premier League.
Morata's agent, Juanma Lopez, and his father, Alfonso Morata, were at the Bernabeu for a 50-minute meeting with Real about the 24-year-old, who has been holidaying in Ibiza and Sardinia after marrying model Alice Campello in Venice last month.
Talks between United and Real have been ongoing for over a month but the two sides have so far been unable to agree a fee. Morata is valued at close to £70m (€80m) by Real.
Our colleagues at Sky in Italy reported last month that United had a £52.4m (€60m) offer rejected by the Champions League and La Liga winners.
If United CEO Ed Woodward can agree a transfer fee with Real, personal terms are not expected to be a sticking point.
Real coach Zinedine Zidane wants the former Juventus striker to stay but the player is desperate for more game time, which the Frenchman can't guarantee.
United leave for their preseason tour of the United States this weekend and so far have bought just one new player this summer - defender Victor Lindelof from Benfica.