Rooms where addicts would be able to safely consume drugs have been suggested for Earl’s Court.
Kensington and Chelsea councillors heard the "safe rooms" could be used by people with "severe" addictions.
Medical supervisors from the borough's drug and alcohol treatment service would be on hand at the sites to oversee illegal substance use if they were introduced.
A report by the council's Chief Community Safety Officer recommended that the authority should "explore the feasibility of the establishment of safe use rooms".
It added: "Depending on the funding available and conditions attached it may be possible to consider the use of alternative residential settings or 'safe use' rooms.
"This would provide a way for addiction to be managed in a controlled environment rather than on the streets."
Earl's Court councillor Linda Wade said the borough had to look for a "fresh way" of addressing persistent drug use in the area.
Kensington and Chelsea council stressed the proposals would only go ahead if funding becomes available and a national plan on how drug consumption rooms would work is explored.
The town hall added it would consider if they could work locally before putting them in place.
London is the area with the lowest number of overdose-related deaths in the country.
However almost 300 people in the capital died from drug use in 2020, according to City Hall statistics.
Last year the London Assembly's cross-party health committee called on the Mayor to pilot drug consumption rooms in London.
Sadiq Khan was also urged to work with the Metropolitan Police to ensure that officers routinely carry naloxone, which is a potentially life-saving drug for someone experiencing an overdose.
Caroline Russell, who chairs the health committee, said the measures could “start to bring down the growing numbers of people sadly losing their lives due to problematic drug use”.
