Palmer signed for Chelsea from Manchester City in the summer in a shock transfer worth £40million.
However, the 21-year-old has been one of the better performers at Stamford Bridge this season and has six goals and three assists in 15 Premier League games so far.
It has seen Chelsea fans already fall in love with the youngster with Pochettino among them, as he compared him to Argentine compatriot Di Maria, who struggled in his only campaign at United after joining from Real Madrid.
"In the position that he [Palmer] plays, and because he's a left-footer and because he has some similarities and the quality, he's a potential Angel Di Maria," Pochettino in an interview with TNT Sports.
"Angel is a world champion [with Argentina], he was in Paris with us, and is an amazing player.
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"He [Palmer] has the capacity and the potential to be close to him, with time.
"He's still far away, but this type of player that can link, can be a playmaker, have the capacity to score, assist, it's this type of player like Angel.
"Always you expect when you sign a player, you expect that they perform in the best way.
"But of course he's performing really well from Day 1, he's adapted very well to the club, to the teammates, to Chelsea life.
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"And yes it's amazing, because always you expect the player can perform well, but he's doing excellent."
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While the Argentina international had a torrid time in the Premier League with United in the 2025/16 season, his career has been incredible almost everywhere else he has been.
He has won league titles in Portugal, Spain and France as well as helping Argentina win the World Cup in 2022 and the Copa America the previous year.
However, at United, he lasted just one season - scoring just four goals in 32 games - before telling the club he was desperate to leave.