Morata has been heavily linked with a move away from Real Madrid this summer, with Manchester United and Chelsea said to be interested.
Sky Sports claim United had a £52.4million offer rejected by Real Madrid for the Spain international, who bagged 20 goals this season.
Red Devils manager Jose Mourinho is said to have turned his attention to Morata, 24, after missing out on Atletico Madrid hitman Antoine Griezmann.
And Rashford, who played second fiddle to Zlatan Ibrahimovic this term, admits Morata is exactly the type of player they need to add the right level of competition at Old Trafford.
Alvaro Morata has been heavily linked with a move to Manchester United
Good competition is important if you want to be successful
"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."
Manchester United line-up next season with Alvaro Morata Tue, June 6, 2017
Click through the gallery for Manchester United's possible line-up next season with Alvaro Morata
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Marcus Rashford welcomes competition at Manchester United
Rashford admits playing alongside the likes of Ibrahimovic and Wayne Rooney has helped him develop his own game.
"The way they (Ibrahimovic and Rooney) think, their mentality towards the game, they are the biggest things that I can take from their game," Rashford added.
"I think with those type of players, whether they are here for the next five years or however long they are here for, you never stop learning from them."