The city also wants the new bridge to be architecturally striking, like San Francisco's Golden Gate Bridge or the Sydney Opera House in Australia.
The project is expected to cost up to $5 billion, a tab Ottawa says will be funded with the help of a private-public partnership and a toll system.
Prime Minister Stephen Harper said last week his government was open to local input on the project.
The federal government oversees the management of a half-dozen major bridges, including three in Montreal.
It pays significant portions of the bridges' upkeep and, when the time comes, for their replacement.
The 50-year-old Champlain Bridge is among the country's busiest.
The City of Montreal outlined its wishes for the new bridge at a news conference Sunday and in an open letter addressed to federal Transport Minister Denis Lebel.
Real Menard, a member of Montreal's executive committee who made the announcement, said the city would like to launch an international architecture competition to encourage an identifiable design for the new bridge.