Sir Oliver Popplewell, the judge who conducted the 1985 Bradford fire public inquiry, says police should look at eight other fires allegedly connected to the then club chairman to "see if there was anything sinister."
A new book claims the fire at Bradford's Valley Parade stadium was one of at least nine blazes at businesses owned by or associated with the club's then chairman Stafford Heginbotham, who died in 1995.
Popplewell's inquiry concluded that the cause was an accident probably started by a spectator dropping a cigarette into the rubbish that had accumulated under an old timber stand, and he stands by the ruling saying there was no evidence of arson.
But he told Press Association Sport: "I don't think it's going to affect what we decided but I think it is important from a public point of view that the police look at the other fires and see if there was anything sinister. It is a remarkable number.
"I think it's important to satisfy people's minds that the other fires are unconnected."
The claims are contained in "Fifty-Six -- The Story of the Bradford Fire" by Martin Fletcher, who was 12 at the time and escaped from the blaze that killed 56 people. He lost three generations of his family, including his father and brother.
Popplewell, now aged 87 and retired as a judge but still actively working in law, added: "No trace of anything was found at the ground of any material which might suggest it was arson.
"To me the mechanics are unbelievable -- why would you do it when the ground was occupied? Even if they show that some of the other fires were arson then it still doesn't actually lead you to conclude that the Bradford fire was also arson.
"Nothing was mentioned to the inquiry about these other fires by the insurers, the fire officers or indeed the police."
Popplewell said the main flaw in the argument that the fire was arson was that the stand involved had no insurance value because it was due for demolition.
He said the fire was examined by experienced and thorough investigators who found nothing suspicious, and he said no question of arson was ever raised in civil legal proceedings.
Former sports minister Gerry Sutcliffe, meanwhile, said the new allegations do not justify a new inquiry into the disaster.
Sutcliffe, MP for Bradford South and deputy leader of Bradford City Council at the time of the tragedy, said he knew Mr Heginbotham "flew by the seat of his pants" in terms of the finances of the club but remains convinced by the conclusion of the inquiry.
Bradford chairman Mark Lawn also said he finds it "hard to believe" the fire at Valley Parade was started deliberately.
He told Press Association Sport: "I feel for the person who has written this book as he has lost his whole family in the fire, but I'm not sure you can start blaming someone who is dead without having proof."
Fletcher says Heginbotham's history with fires, which he claims resulted in payouts totalling around £27 million in today's terms, warranted further investigation.
"Could any man really be as unlucky as Heginbotham had been?'' he asks.
A minute's silence is due to be held at every Premier League and Football League match on Saturday April 25 to mark the forthcoming 30th anniversary.