Milan general manager Marco Fassone confirmed at the weekend that Morata, Pierre-Emerick Aubameyang and Andrea Belotti were on their shortlist, and the Madrid man now appears to be the frontrunner, with La Gazzetta dello Sport reporting that they are "on the verge" of sealing a deal.
The fee agreed between the two clubs at that time was £29m but the 26-year-old 'keeper would now cost at least double that amount, barring any unlikely swap involving Kroos.
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Milan have already agreed one of the most impressive signings of the summer after securing a deal for Italy international Bonucci from Juventus.
The Telegraph claimed that United value him in excess of £60m and De Gea would be keen on a return to his homeland if an offer finally arrives.
Romelu Lukaku failed to open his account but Marcus Rashford scored twice with Marouane Fellaini, Henrikh Mkhitaryan and Anthony Martial all on the scoresheet.
There was lots of speculation linking Morata with Manchester United and ever Herrera admits that he was expecting to line up with his compatriot at Old Trafford next season.
"Evidently we are still thinking of doing something in that position".
"I don't like to speak about players who aren't ours because Morata is not our player". It is simple. It is a shame.
"It is a question for Florentino [Perez]".