The former Hammers boss and player has been regularly linked with a return to Upton Park during Allardyce's difficult spell in charge of the East Londoners.
The former Queens Park Rangers boss enjoyed relative success at West Ham having led the club to its highest ever Premier League era finish of fifth and into Europe during his tenure. But he upset some West Ham fans by taking the job at Tottenham Hotspur and was jeered on his returns to the Boleyn.
The 68-year-old Poplar born boss, who is said to be friendly with Hammers joint owners David Gold and David Sullivan, was expected to announce his retirement when he walked out of QPR earlier this season, but he has since insisted he would be back in management at the earliest opportunity.
One club he did rule out moving to back in February, though, was West Ham.
He told Claret and Hugh in an exclusive interview that there was 'no chance' of him making a shock Upton Park comeback.
"Tell everybody to keep their money in their pockets. It’s not going to happen," said Redknapp.
"I don’t even know what’s going on at the club as far as Sam Allardyce is concerned. I read the reports but we will have to wait and see. What I do think is he has done a great job but predicting what is likely to happen in this game is a fool’s game. However, should a vacancy become available at the Boleyn I can promise you I won’t be filling it," he added.
But a clip of Redknapp being asked by Arsenal legend Paul Merson what he would do if he was offered the West Ham job when appearing as a guest on Sky Sports' Fantasy Football Club suggests an apparent U-turn.
The former Portsmouth and Southampton manager said he thought the club 'would be mad' to get rid of Allardyce, but in a change of tack, Redknapp replied that he "The club is in my blood... I couldn't sit here and say I wouldn't want to manage West Ham again because anybody who has played there would love to go back there, it's a great club."
Redknapp had a 37% win ratio from 327 games over seven years at West Ham while Allardyce has a 38.29 win percentage from 175 games over the last four years.
Sullivan, Gold and Allardyce have always insisted talks over Big Sam's future at the club would be held at the end of the season, as is club policy.