Transport for London (TfL) is holding a public inquiry into the possibility of extending the Northern Line.
If approved, with a relevant funding package, construction could start as early as 2015, with two new stations launching in 2020. The investigation is a formality for projects this size as part of the Transport and Works Act Order.
The organisation believes such a scheme will help regenerate the Nine Elms area and remove pressure from existing areas, such as Vauxhall station and south of Kennington on the Northern Line itself.
TfL's managing director of planning Michele Dix said: "If this transport link goes ahead it would create access to the tube for thousands of people in south London as well as helping to support new jobs and homes in the area."
It states the project will cut journey times between the City and Battersea areas by 15 minutes.
Three public consultations have already been held, which confirmed strong support for the plans, while the inquiry itself will last for approximately four weeks.