The public consultation starts today and finishes on Friday 17 June.
The Mayor's transport strategy supports an externally funded extension of the Northern line to support development in the surrounding area.
The Tube extension is part of a package of transport measures that would enable the regeneration of the GLA's wider Opportunity Area which covers Vauxhall, Nine Elms and Battersea.
If the extension goes ahead two new Tube stations would be created, one at Nine Elms and one at Battersea allowing easy access to the Tube network.
The Mayor of London, Boris Johnson, gave the go-ahead for the redevelopment of Battersea Power Station last year - the approved plans include a Tube station at the power station but the full development is dependent on the extension of the Northern line.
The construction of the extension is subject to external funding and the award of a Transport and Works Act Order by the secretary of state for transport. The draft order is expected to be submitted by autumn 2011.
In the first stage of the public consultation process in 2010, local residents were asked by Treasury Holdings to comment on four possible route options, all of which ran from Kennington to Battersea Power Station.
The preferred option was the route via south Nine Elms.
Subject to funding and further planning permission the Northern line extension could be completed in 2017.
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