Allardyce guided the Hammers to Premier League safety but he has been the subject of criticism from supporters and reports on Thursday suggested he was facing the sack after Sunday's clash with Manchester City.
But Nolan, who played under Allardyce at Bolton, says the squad is firmly behind their manager and issued a passionate plea to the Hammers board to stick by him.
"It shocked a lot of the boys," he said. "We found it all quite surprising to be honest and we are still quite shocked that people can write that stuff.
"If you ask anyone in that dressing room, the gaffer has got the full backing of every one of us.
"It's a sad occasion when we are talking about him getting sacked after the magnificent job he has done over the last three seasons and I've been a part of that with him.
"I've seen the difference he's made from when he first walked in - the state of the club from then to what it is now - I'm sure the owners would recognise the magnificent job he's done.
"I firmly believe and the gaffer firmly believes we could have done a lot better, we know that, but there's been some massive obstacles.
"So I'd tell the chairman you've got to stick with him because you've only got to look at what he built at Bolton.
"He took us from a Championship side to Europe in five years and his record speaks for itself when he's given time to develop a club."