The player is for sale for £61million although the Red Devils will try to get him for less.
Morata has been one of the most sought after players in recent summers, largely due to his clinical presence inside the area, with the Spaniard contributing 20 goals in a bit-part role last term.
After the drawn-out pursuit of Antoine Griezmann failed and considering Romelu Lukaku is expected to re-sign for Chelsea from Everton rather than make the switch to Old Trafford, that leaves a pretty short list.
United goalkeeper David De Gea, a long-term target of Real's, was not included in the bid.
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The latest development will prove to be something of a hit for United, but the Old Trafford-based club will not be deterred in their pursuit of the Spain global as they look to bolster their forward options in the close season.
"The way they think, their mentality towards the game, they are the biggest things that I can take from their game", he said of Ibrahimovic and Rooney.
"I know for certain that Manchester United are the only club that want Morata, nobody else", Paco Gonzalez of Cadena Cope noted.
After gaining a Champions League winners medal - it seemed like it would be the flawless final chapter in Alvaro Morata's Real Madrid career.
"I'm happy here, it's my dream to be here, we've just won the Champions League and I'm not thinking about anything other than celebrating".