Allardyce, 63, is without a job after leaving Everton in the summer and one better reckons he will take over at Carrow Road.
But Norwich's current boss Daniel Farke seems safe in his job after taking over in May 2017.
The Canaries sit ninth in the Championship, just one point outside the play-off places.
Despite this, someone still tried to lump a huge sum on Big Sam to take over.
It means Allardyce is now the 10/11 odds-on favourite to be the next Norwich boss with Paddy Power, with whom the punter tried to place the bet.
The bookmaker said: "A Norwich punter has tried to place a big bet on Big Sam taking over at Norwich, despite no talk previously about the eventuality.
"He's always said he's a Championship-winning manager – now is his time to demonstrate it rather literally."
Allardyce began his managerial career way back in 1991 and took charge of nine clubs including Bolton and West Ham where he won promotion from the second tier via the play-offs before being appointed England manager in 2016.
He famously lasted just one game before being sacked by The FA and returned to club football to manage Crystal Palace and then Everton.
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