The SNP want to bring the underground network under council control and take it away from Strathclyde Partnership for Transport (SPT).
Should the party oust Labour from the leadership of Glasgow City Council on 4 May, they say they have ambitious plans for the 120-year-old underground network.
Currently, the Subway serves the centre, West End and south west of the city.
The SNP has said it will investigate possible extensions to the east and north.
To fund the work the party said it would look at new ways of raising cash rather than relying on capital grants from the Scottish Government.
The Subway is currently undergoing a £288 million refurbishment including revamped stations, new track and signalling, and, eventually, new trains.
Kenny McLean, SNP councillor and candidate for Partick East-Kelvindale, which includes Partick and Kelvinhall stations, said further improvements could be made.
He said: “It is our view that the Subway would be able to contribute more to economic growth in the city and be more responsive to the city’s people and visitors if it were controlled by the City Government.
“We are also confident that more can be done with the Subway to connect communities.
“We are also not afraid to build on the ongoing renovation of the Subway.”
Building new tunnels and stations under city streets would cost hundreds of millions of pounds.
Mr McLean added: “We will look at possible extension of the Subway and consider innovative funding methods, such as City Bonds, to fund this work.
“The subway is over 120 years old. It is high time that we look to connect communities in the north and east of Glasgow.”
The first move would be to take the Subway out of the hands of SPT and bring it under the control of the city council, which the SNP is referring to as the City Government.
Mr McLean said: “Glasgow’s Subway is a cherished asset of the city. It has, for decades, been managed by SPT on behalf of the city.
“However, an SNP City Government will take steps to change this. We will work with the Scottish Government and SPT to bring control of the Subway back into the control of the City Government.
“The Subway is entirely within Glasgow, it makes sense that the network is maintained by the City Government.”
Extending the Subway beyond the current 15 station, twin-circle network has been mooted before.
In 2007, the then SPT chairman, Labour councillor Alistair Watson, said there would be an extension into the east end in time for the Commonwealth Games, but the plans never came to fruition.
After the city was awarded the games, Mr Watson said: “We will deliver the East End extension for 2014. I am being unequivocal about that.”
The plan then was for a link between the Games venues at the SECC, the Emirates arena and Celtic Park. This would have been connected to the main inner and outer circles via Argyle Street at St Enoch.