United themselves pursued Morata earlier this summer but failed to reach an agreement over a fee.
Mourinho subsequently landed Antonio Conte's top target Romelu Lukaku instead for £75m.
Both have now strengthened up front ahead of the new season.
But when quizzed on Morata's switch to Chelsea, Mourinho was not only unfazed but unsurprised too.
GETTY
Manchester United boss Jose Mourinho is not bothered by former target Alvaro Morata joining Chelsea
I'm not interested in what Chelsea does, really
Jose Mourinho
Chelsea have been needing to add a striker with Diego Costa set to leave, having been told by Conte he is no longer in his plans.
On Morata, Jose Mourinho said: "I'm not interested in what Chelsea does, really.
"With Chelsea it was obvious they were going to sign a striker after the situation with the manager and Diego (Costa).
"We needed a striker, so yes, we needed one even with Zlatan in his best conditions, we needed one to give cover, give options.
"Him (Ibrahimovic) and Marcus was not enough, especially after the injury.
"But we got a big player, a player that I can't compare with what he was a few years ago, because he worked with me for a few months and his development was very good."
New Manchester United hitman Lukaku is already off the mark, having netted his first goal for the club in their friendly against Real Salt Lake on Tuesday.
The Red Devils continue their US tour with a clash against Manchester City tomorrow (3am).
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