Spurs confirmed the 65-year-old's departure yesterday, which Redknapp – who has no intentions of retiring – felt was inevitable even if he had secured Cham-pions League football.
Everton manager David Moyes and Wigan boss Roberto Martinez are leading candidates, along with former Chelsea head coach Andre Villas-Boas and Rafael Benitez.
Redknapp insists the current squad – which includes the likes of Gareth Bale and Luka Modric, both linked with moves away from White Hart Lane – can go on to bigger and better things, despite having faded badly over the final weeks of a campaign which had for so long promised so much.
"I leave behind some fantastic players. The only disappointment I have is that I think it was a team which could have gone on and eventually won the Premier League in the next year or two," Redknapp told reporters.
"I just wish I could have been able to see that through and be part of that because they have some fantastic players there."
Redknapp felt yester-day's outcome was always on the cards, regardless of how the campaign ended.
"We missed out on third place by one point in the end, but that is how it goes," he said.
"I think the same outcome would have happened, the chairman would have gone down the same road."