Pochettino was appointed the Tottenham head coach in the summer of 2014 and has a contract until June 2019.
Former Spurs midfielder Redknapp believes that the North London outfit should tie down the Argentine boss to a new long-term deal.
The former Liverpool man has also suggested that Manchester United and Chelsea should be looking at Pochettino in the summer.
“If I were Daniel Levy, I would be knocking on Mauricio Pochettino’s door with a huge new contract,” Redknapp wrote in The Daily Mail. “Tottenham have had six managers in the last 10 years. Now they have one they simply have to keep.
“This summer it looks like Chelsea and Manchester United will be looking for new managers. They would be mad not to look at Pochettino. He ticks every box an owner requires.
"He plays good football, gives kids a chance and gets his teams so fit and organised. His substitutions at the Etihad were attack-minded and won the match. And, importantly, it’s not all about him. He proves you can still be a top boss without being arrogant.”
Pochettino has done a really great job at Tottenham, and he could even guide the North London outfit to the Premier League title this season.
Spurs have arguably been the best and the most entertaining team to watch this season, and the former Southampton manager deserves the plaudits that he is getting at the moment.
While United and Chelsea may be attractive prospects, perhaps it would be best for Pochettino if he remains at White Hart Lane beyond the summer.
At Tottenham, the 43-year-old has built a team in his own image, and he is very popular among the fans.