The Real Madrid star has been tipped to leave the Bernabeu this summer, with the Red Devils keen on the 24-year-old striker.
Starsport revealed yesterday that United will make a take-it-or-leave bid of £60m for the former Juventus man.
The Red Devils have focused their attention on Morata after accepting Everton talisman Romelu Lukaku will join Chelsea.
United are confident of striking a deal with the La Liga champions for the Spain international.
And according to the Manchester Evening News, Mourinho has told his close pals of his admiration for Morata.
MEN say the United boss is convinced the Real star is the perfect striker for the Red Devils.
Mourinho feels Morata has the physical attributes to handle the demands of the Premier League, just like his previous strikers Didier Drogba, Diego Costa and Zlatan Ibrahimovic.
Morata's agent Juanma Lopez has been vocal on his client’s future, revealing he has become frustrated at Real.
"He does not want a season like this again. It was a great season, but he wants to play more," said Lopez.
"The player will take a clear and definitive decision in the coming days. I have not yet met with the representatives from Real Madrid.
"Alvaro is a player who wants to play a more important role. He wants to play more. Which is normal for an attacker who has scored 19 goals. It is too little."
