Shaw has kept his head down and impressed manager Jose Mourinho in recent weeks with his attitude to training, although the former Southampton academy graduate still found himself on the subs' bench until late in the League Cup victory over Swansea on Wednesday night.
However, a number of injuries allowed the youngster to make just 16 Premier League appearances during his debut campaign in Manchester, before a horrendous double leg break suffered in a clash with PSV Eindhoven at the beginning of the 2015-16 campaign saw the English global miss the remainder of his second season with the club.
Mourinho was critical of Shaw last season, suggesting the England global needed a "better understanding of the game".
Pochettino insists they have moved on from the issue and his United counterpart certainly feels things have worked out well, having instead signed Matic from former club Chelsea for an initial £35million.
He claims that Pochettino "really wants me to play under him again".More news: Microsoft passes $80 per share in after-hours trading after blow-out quarter
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"I just think l, normally, we have performances at home, normally we trust our game, and yes, the results we can say are positive at home".
Pochettino's new book, Brave New World, also features quotes in the epilogue from United left-back Luke Shaw, who reveals the Tottenham boss used to call him "son" during their successful spell together at Southampton.
"I don't speak about injured players, so don't ask me about Harry Kane", the Portuguese added, before listing United's own lengthy injury list.
The 22-year-old full back has been linked with a reunion with Pochettino at Tottenham and the England worldwide has opened the door to such a move. Because of his words? We were one of the best footballing teams in the league.I do hope that I can play for him again one day. Luke Shaw was just honest. "But he is in the squad, he works and maybe the opportunity comes".
"So for me they are flawless words that show Luke Shaw's character in relation to the people that he was happy with". In this moment I can't give him that.