The former Spurs striker made his own switch between two Premier League rivals in his playing days, going on to form part of the Red Devils’ 1999 Treble-winning squad.
A similar move is now being mooted for a highly-rated coach, with United yet to make a decision on who will be appointed as the permanent successor to Jose Mourinho.
Ole Gunnar Solskjaer is staking a serious claim to staying on past the end of his interim spell, while the likes of Zinedine Zidane and Antonio Conte have been billed as other options.
Sheringham sees no cause for Pochettino to consider filling the hot-seat at Old Trafford, with there still plenty for him to achieve with a Tottenham side that he has helped to turn into serious contenders for major honours.
The ex-England international told the Daily Mail: “I left Tottenham to join Manchester United in 1997 for one reason — ambition. The club was settling for mediocrity at the time and I did not like it. It was as simple as that.
“Now Mauricio Pochettino has been linked with United — but he has no reason to leave. He is at an ambitious club now, a club that is going places.
“Tottenham are on the up, on and off the field. They have a tremendous team and in Harry Kane they have one of the best strikers in the world. The club have Kane and Kane has Pochettino.
“Why would either want to leave? Or need to leave? They are doing well in the league, they will soon move into a fantastic new stadium and the team is getting better and better under Pochettino. It is a completely different set-up to the one I left.
“Yes, you could argue that United are the biggest club in the world and if Pochettino is only interested in money then obviously United might appeal, but I don't think it is about money with him.
“He is ambitious, he is developing a great team and he is not afraid to bring in young players. He has a great eye for a player.
“He has proved to be a fantastic manager and, with the new stadium coming, why would he want to leave everything he has built?
“He has put together what is becoming a great team with a lot of very good players in his squad. They are playing his way and they are getting better.
“There is no reason to think he will be better off anywhere else. The Tottenham I left is a long way from where the club is now. I am sure he will stay.”
That deal is set to take him through to 2023 and he has offered no indication that he is looking for a way out, despite regular links to the likes of United and La Liga giants Real Madrid.