Silva was pivotal for the French side as they won the Ligue 1 title ahead of Paris Saint Germain.
The Portuguese attacking midfielder scored 10 goals and had as many assists for Monaco in 54 appearances for his club.
Mourinho is frequently linked with signing players from his homeland but the Manchester United boss doesn't think Silva will be moving to Old Trafford despite his quality.
He told Portuguese newspaper O Jogo: “Will Bernardo Silva be with us next season? I don’t think so, honestly.
Jose Mourinho celebrates in style after Manchester United's Europa League win Wed, May 24, 2017
Jose Mourinho was very happy after Manchester United won the Europa League!
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Jose Mourinho celebrates in style after Manchester United's Europa League win
Will Bernardo Silva be with us next season? I don’t think so, honestly
"But you never know, good players are always welcome here.”
Following United's Europa League win over Ajax, which guaranteed their qualification for the Champions League, Mourinho said it is now down to executive vice-chairman Ed Woodward to sign the players he wants in the transfer window.
“Ed Woodward has my list, what I want, what I would like for more than two months,” he told BT Sport.
“So now it’s up to him and the owners.”
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Bernardo Silva was excellent for Monaco this season
Mourinho later added on MUTV: "I wish Mr Woodward all the success in his work because now it’s time for me to disconnect, because I’m very tired.
"I am going to land in Manchester, I am going to get a car to London, then to Portugal. I don't care about football for now. Now I am on holiday.
"I don't want to see any international friendlies, I am selfish. I can't do it. For me, enough is enough.
"It has been a very hard last few months, we were short of numbers. But with three trophies in one season and the Champions League, I am very happy in my most difficult season as a manager."