Starsport understands the Red Devils are keen on the 24-year-old and want him to lead the line at Old Trafford next season.
Jose Mourinho is an admirer of the Spain international, who he managed during his time at the Bernabeu.
And according to the Daily Express, Morata has made up his mind to join United and a deal is done.
They say Mourinho has convinced the striker he will be a hit in the Premier League.
Morata left his honeymoon early to hold talks with Real president Florentino Perez.
And those negotiations have sped up the transfer, with the La Liga champions set to lower their £70m asking price towards the £60m range.
The Express add that the two clubs are close to an agreement for Morata.
Morata struggled to get game time under Zinedine Zidane last campaign.
Despite making limited appearances, the striker still netted 20 goals in all competitions.
Morata would become United’s second summer signing.
Mourinho has already landed Benfica defender Victor Lindelof and has other targets he wants to bring to Old Trafford.