Former Newcastle boss Allardyce has never won over the West Ham fans, despite getting the club promoted, and his time is about up.
The Sunday People claims Redknapp, who managed the Hammers between 1994 and 2001, could be asked to make a sensational return should Allardyce depart when his current deal expires at the end of the season.
Redknapp is currently trying to mastermind a great escape with QPR, who looked certain to be relegated from the Premier League when he took over in November.
But they are now seven points adrift of safety, and if QPR go down ... West Ham will make their move.