Speculation over the Spaniard's future at the Bernabeu has been rife in recent months.
Morata has struggled for game time under Zinedine Zidane this season with Karim Benzema and Cristiano Ronaldo keeping him out of the starting XI.
However, the 21-year-old has still scored 23 goals in all competitions for Los Blancos and that has led to plenty of interest from Europe's top clubs.
Chelsea, Manchester United and AC Milan are all understood to be competing for his signature.
Alvaro Morata s attracting interest from Chelsea, Man Utd and AC Milan Alvaro Morata's next club: Where could the Real Madrid ace go next? Tue, May 16, 2017
Where is Alvaro Morata tipped to go next? Odds provided by Paddy Power
Play slideshow Getty Images 1 of 11
Where could Alvaro Morata go next? Odds provided by Paddy Power
Express Sport understands Morata is on Antonio Conte's wishlist should Diego Costa depart the club this summer.
But Manchester United boss Jose Mourinho is also a big fan of the Spain international and is attempting to lure him to Old Trafford,
Milan have been leading the race to sign him though, with the Italian club said to have offered him a deal worth £125,000 per week.
And Italian publication Gazetta dello Sport claim the speculation could come to an end today with Morata set to make a decision on his future.
Alvaro Morata is under contract with Real Madrid until 2021
Get Quotes on Home Insurance
Following the conclusion of Madrid's season on Saturday as Morata helped his side to Champions League glory, the forward will discuss his next move with his family.
And his comments after the final suggest a return to Serie A may not be on the cards.
"I don’t know anything about Milan [interest]," Morata said.
"I read these things in the papers but don’t know anything about them."
He added: "I think that it doesn’t depend on so much on me if I want to stay, I am happy here, my dream is to be here and right now I’m not thinking about anything but celebrating."