Last month, the council voted to underwrite the potential £33 million cost of building the station.
It hopes that it can create a commercial development above the station, charging developers through section 106 deals to recoup the cost of the development.
The council has written to mayoral agency Transport for London (TfL), which is preparing a business feasibility study for the station, with its proposal to underwrite the project.
In a letter last week to local paper the Kensington & Chelsea Chronicle, Malthouse, who is the London Assembly member for Kensington & Chelsea, wrote that the case for the station was "overwhelming" and would "transform the area for residents and tourists alike".
He said: "I am writing to give my full support to the proposal to create a Crossrail station at Kensal Green.
"I will be pressing [London mayor Boris Johnson] and TfL to bring this project to fruition."
Other key supporters of the campaign for a Kensal Green Crossrail station include the National Grid, retailers Sainsbury’s and Cath Kidston, and Jenny Jones, Green Party member of the London Assembly.