The flurry of activity has surprised bookmakers Paddy Power, who said that punters are still laying down large sums despite odds being cut severely.
On Thursday night Redknapp was 50/1 with the bookmaker to be the next Premier League manager to leave his job. They have since slashed the odds to just 2/1, and this despite Tottenham currently lying in fourth place.
Darren Haines, a spokesman for Paddy Power, said: "There seems to be no rhyme or reason to this one and frankly its left us baffled.
"But no matter what price we cut Redknapp to punters keep backing him. Surely they don’t think he’s going to go back to save Portsmouth for a third time?"
William Hill spokesman Graham Sharpe added: "It is probably a bandwagon effect as ususal, based on unsubstantiated gossip, but in volatile markets of this nature you can't afford to take a chance and we are being inundated with calls from punters wanting to bet that Harry will be the first to go."
Hills make Paul Hart 11/10 to be the first out, with Phil Brown at 5/4 and Redknapp 5/1 third favourite.
Redknapp is due to give a scheduled press conference this afternoon ahead of the weekend game against Bolton.