Parkrun is a national charity that organises 5k running events up and down the country.
But concerns have been raised recently in places including Daventry about the effects constant runs have on open spaces.
Wandsworth Council says the Battersea Park route would avoid grassed areas and ensure runners keep to paved avenues.
The borough has been home to another weekly Parkrun event on Tooting Common since 2016.
A consultation on the Battersea run has now been launched.