Writing in British newspaper "The Sun", Redknapp said Manchester United have fallen into chaos, but that there is no better time than now for Pochettino to take charge.
Managers see jobs like this as an opportunity not to be missed, he added, because the only way from their current position is up.
Read also
Hossam Hassan's dismissal is not the surprise: his appointment is
Zidane reacts angrily when asked about Mbappé: Nonsense!
"Things can only get better for Manchester United with Pochettino," he continued. "He won't take them down, of course, he won't do that."
Related Topics
Redknapp recalled his own experience at Tottenham. He took over in October 2008 after a disastrous start to the season, and he did not hesitate to accept the task.
"When the Tottenham job was offered to me, and they were in trouble after the worst start in their history, it was a no-brainer," he said, explaining that this is how managers think when weighing up such opportunities.
Taking over United straight after Ferguson's departure, by contrast, would have been a completely different challenge. The manager in that case would have found himself required to improve a team that already carried a huge legacy and a high level of success.
He cited David Moyes, the man Ferguson chose to succeed him. It did not last long, and everyone knows how things ended.
Redknapp revealed a friendly relationship with the Argentine. The pair share the same birthday, the second of March, and they met on it when Pochettino was Southampton manager and he was in charge of Queens Park Rangers. "We won!" he added.
The two also worked together at the charity match "Soccer Aid", and Redknapp described him as a very clever and knowledgeable man.
Pochettino and his assistant Jesús Pérez can revive the atmosphere at Old Trafford and the training ground, he said, and bring some smiles back to the club. But they also possess footballing intelligence and an ability to build teams, two elements that will be essential in the coming phase.
One problem looms largest for the Argentine: how far United's management are prepared to go in giving him the players he needs to succeed.
The current squad is "shocking", Redknapp said. A great manager cannot do much with poor players, and any manager, whatever his abilities, will be beaten without the right elements.
Those running Manchester United drew sharp criticism. He finds it difficult to understand some of the people in charge of appointing managers, and he reckons they bear a large part of the club's problem, because of the confusion in signings and the erratic decisions over coaching staff.
He also hit out at the way United's management handled Carrick's departure, describing what happened as shocking. The former manager had been a great player for the club and a wonderful man, he pointed out, but was treated very badly, with news of his departure leaked before its official announcement.
