It is understood that the borough's planning officers are happy for Parkview International to knock down and rebuild the chimneys. This could lead to the famous white stacks being absent from the London skyline for up to three years.
Parkview's application comes despite a recent report by the World Monuments Fund and the Twentieth Century Society (C20) that claims demolition is unnecessary.
C20 has deep reservations about the proposed planning application, though English Heritage has expressed satisfaction that demolition is necessary.
The news comes just days after Channel Four viewers voted the power station one of the top 10 attractions nationally as a 'unique and defining structure', according to local conservationist group the Battersea Power Station Community Group (BPSCG).
BPSCG chairman Brian Barnes said: 'Wandsworth council is going to approve a plan by Parkview to demolish the four chimneys that we are convinced is a prelude to complete demolition, so that [Parkview chief] Victor Hwang can build luxury flats all along the river frontage.
'Our suspicions are founded on the refusal of the council and Parkview to even consider an alternative report by a team of three companies of concrete experts brought together by C20 and World Monuments Fund, who have revealed that the chimneys can be repaired for half the cost of demolition and rebuilding.'