A ban on football fans drinking in the stands during matches is outdated, discriminatory and should be scrapped, Andy Burnham said.
The Prime Minister said it was unfair for football fans to be singled out when supporters of other sports were able to drink while watching their teams.
The ban was put in place during the 1980s when concerns about hooliganism were at their height and covers the top-five tiers of English men's football.
But Everton fan Mr. Burnham said it was a measure from "an era when football was very different."
The Football Supporters' Association (FSA) welcomed the Prime Minister's words and said successful pilots of alcohol in the stands had been carried out in the women's game.
But police chiefs warned it would be "incredibly rash" to make changes without proper consultation with forces.
Mr. Burnham told reporters: "I don't think it's fair for football fans to be singled out in that way and I made that point.
"I think that legislation dates to an era where football was very different.
"And I do believe there is a case to remove that discrimination. There are different ways it could be done, perhaps on a trial basis.
"But I'm not going to back away from what's been a long-held view of mine. I don't see how it can be fair that some supporters of one sport can be treated differently from others."
The Sporting Events (Control of Alcohol) Act 1985 prohibits drinking in sight of the pitch in England and Wales in the top-five men's leagues.
FSA chairman Tom Greatrex said: "The FSA has always argued that it's unfair to criminalise football fans for having a pint while watching the match -- especially since you can sit in the same seat drinking alcohol whilst watching an Oasis gig or rugby league.
"Many clubs are in favour as well. WSL and WSL2 ran a successful pilot, meaning fans can now drink in the stands at many grounds, while the EFL has long supported a trial.
"We welcome the Prime Minister's comments and totally agree that the legislation is outdated and deserves to be reviewed. We look forward to being part of that consultation."
A UK Football Policing Unit spokesman said police chiefs would welcome a meeting with Mr. Burnham to "explain the challenges these proposed changes would bring to policing and the safety of staff and fans."
The spokesman said: "Other sports simply don't see the violence and criminal behaviour from their supporters that football does, albeit a minority, with alcohol often playing a significant part in violent and disorderly behaviour.