Spurs boss Pochettino suggested in a recently released book that he was frustrated with Mourinho after he went out of his way to embrace Dier following Tottenham's game at Old Trafford last December.
Shaw had the most successful season of his career under Pochettino at St. Mary's before he left to join United and Mourinho was very understanding of his comments, describing them as the "perfect words".
But Mourinho, whose side play fellow title challengers Tottenham at Old Trafford on Saturday, said while it will be hard for Shaw, he does have a future under him.
Mourinho won the Europa League and EFL Cup in his first season at Old Trafford and will hope to build on the encouraging campaign this term with his side returning to the Champions League.
Rose made his first appearance of the season as Spurs drew with Real Madrid at the Bernabeu last week while he played nearly the entirety of their EFL Cup defeat to West Ham United on Wednesday evening.
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"I am always disappointed when a player, because he has a new manager, the new manager becomes the best and the old manager becomes very bad, and football is full of examples of lack of character".
"I probably have the player I didn't think it was possible to have, but we got the player I really wanted".
"The manager that helped him to come to the first, to come to the best moment of his career is a manager that do not forget he likes a lot and that maybe one day he would be reunited again so for me the ideal words that show Luke Shaw character in relation to the people that he happy with". I do hope that I can play for him again one day.
"We are a team who want to compete, who are competing and then the results are the results".
Mourinho berated his team in the away dressing-room at the John Smith's Stadium last weekend in the wake of their first Premier League defeat of the season.
"He is in the squad, he works and maybe the opportunity comes".