The Real Madrid star has been linked with a huge summer move to Old Trafford.
Starsport understands United and Chelsea are keen on the 24-year-old striker.
The Spain international has struggled to get game time under Zindedine Zidane but did impress in minimal appearances.
And United star Rashford has responded to rumours of Morata moving to Old Trafford, claiming the Red Devils need to sign top players to make competition for places.
"At a big club you are going to attract big players and that's what we want," Rashford told Sky Sports when asked about Morata.
"Anyone who can come in and help the club win trophies, which is the ultimate aim, they are the players we want to bring in.
"Good competition is important if you want to be successful."
Jose Mourinho will splash the cash this summer with Champions League football returning to Old Trafford next season.
United had been tipped to sign Atletico Madrid star Antoine Griezmann but the Red Devils have cooled their interest in the France star.
Morata and Everton talisman Romelu Lukaku now top their summer wish list.
