With the Red Devils having taken the decision to part with their Portuguese coach, there is now a high-profile vacancy at Old Trafford.
Ole Gunnar Solskjaer has taken the reins on an interim basis , with the former United striker returning to England on a short-term agreement.
Various candidates have been mooted as a more permanent replacement for Mourinho, with Pochettino among them .
He has enjoyed a productive spell in the Premier League with Southampton and Spurs, which has helped to raise his profile, but Redknapp feels he would be making a mistake in taking on a “difficult” job in Manchester.
The former Tottenham boss told talkSPORT: “He’s done a great job at Tottenham.
“I love him. I like his character and his personality and he gets the best out of his players.
“Would he leave Spurs to go to Manchester United at the moment? He’s got a better team at Tottenham, by far.
“I think Daniel Levy is looking after him very well, he’s got to be up there with the top wage earners and he maybe sees Tottenham as a team he can win trophies with.
“Man United is a massive club, but I think in his situation when he’s building such a good team at Tottenham – there’s a lot of work to be done at Man United to build a good team. Where do you find the players, it’s getting more and more difficult.
“They are way short of being anywhere near the top couple of teams at the moment.”
Pochettino currently has Tottenham sat third in the Premier League table, 13 points clear of sixth-placed United.
He has also guided Spurs into the semi-finals of the Carabao Cup, with a 2-0 derby victory over Arsenal on Wednesday carrying them into the last four .
Another all-London clash awaits at that stage, with Chelsea representing the next hurdle to be cleared by a side chasing down a first major honour under their highly-rated coach.