Now, with the team under pressure at the business end of the season, many hope that he'll hurry up and accept the England job, so that the club can appoint a new manager who can kick on even further.
And over at Newcastle, Alan Pardew's appointment as manager in 2010 was greeted in disbelief and utter contempt - Christ, the guy couldn't even get Southampton out of League One!
But that's all history now, as Pardew has Newcastle punching well above their weight, and the club could well end up above Tottenham come the end of the season.
So, with Redknapp surely on his way to take on the impossible challenge that is England, who are the good bets to take over from him ?
Jose Mourihno ? No way, Jose. Sorry Spurs fans, you just ain't a big enough club and won't have enough money to splash around to suit his needs.
Brendan Rodgers ? Sure, Swansea are playing some good football, but one Swallow doesn't make a summer, and it will be a huge gamble to go for someone with limited experience (just ask Reading fans).
But what about Pardew ? He's a London lad (born in Wimbledon), and, apart from Newcastle, has only managed clubs 'down South' (Reading, West Ham, Charlton and Southampton). Older and wiser now, Pardew could be a good choice to replace Harry, especially if he feels that, come the end of the season, he has taken Newcastle as far as they can go under the current management.
image: © apasciuto