The two raised roadways were built in the 1970s, designed to be part of a freeway system that was abandoned after public opposition.
Many now see the viaducts as a barrier, cutting off neighbourhoods from the False Creek waterfront and from each other.
Mayor Gregor Robertson says he believes removing the viaducts could be the best way to develop the area in the future.
"The city can take what is a dead zone and transform it into quality of life and economic opportunity as well," he said.
The plan being considered by council would allow for extensive development, including the construction of hundreds of condos and affordable housing units.
City staff say replacing the viaducts with a revamped Pacific Boulevard and an expanded grid would also reduce traffic in the area.
Coun. Geoff Meggs said it's time to connect parts of the city that are currently divided.
"What would happen is that this part of the city, which is surrounded by some of our most important heritage neighbourhoods, but also our growing neighbourhoods — Granville and Yaletown — would all be connected and have a big park in the middle," he said.
According to city officials, tearing down the viaducts would cost $135 million, while leaving them up would cost $120 million due to necessary maintenance.
Waiting longer could drive the price higher, since developers are already building around the viaducts, reducing the number of options for future development.