It is one of several infrastructure projects thought to have been earmarked for by George Osborne – although the majority of the funding for the new extension would be from the private purse.
Planning approval to build two stations on the Northern Line as part of a £5.5bn revamp of Battersea power station was granted by the mayor, last year.
Spending plans will be outlined in the Treasury's Autumn Statement today.
The redevelopment of Battersea Power Station will include shops, office space and leisure facilities, and the construction of 16,000 homes.
However, its iconic chimneys will be demolished and rebuilt, as they are "beyond repair".
The Grade II listed building opened in 1933 and generated power until 1983.
Restoration of the main power station, including rebuilding the chimneys, will be completed by 2016.