The Wirral-born cyclist says plans have already been trialled in Paris, where it is claimed the number of collisions has been cut.
He says it often safer for cyclists to skip red lights, and a rule change may even encourage more people to cycle.
However, road safety charity Brake said the idea was "dangerous and foolish".
Mr Boardman, who won a gold medal at the 1992 Olympics in Barcelona, said: "Safety-wise, it's not an issue.
"The problem is people get really upset when someone is seen to be queue-jumping."
He added: "It's about people saying 'that's not fair, that's not right, that's not the rules'."
Mr Boardman, 46, called for the rule change to be introduced in stages, with signs put up to make other road users aware.
Speaking to BBC Radio Merseyside, he added: "If we change the rules and say it's ok for cyclists to do this, it makes it more appealing for people to ride bikes, because it's safer and quicker."
Gary Rae, campaigns manager for Brake, dismissed the idea and said the charity is calling on the government to invest in more cycle lanes.
He said: "A cyclist, like any other road user, should always observe the highway code. Taking the decision to ignore a red light is both dangerous and foolish.
"To help reduce deaths and injuries, we believe that the government needs to commit at least Â£10 per head nationally for cycling infrastructure, to create segregated cycle lanes."
Olympic champion Chris Boardman says Liverpool should consider becoming the first British city to allow cyclists to legally skip red lights.