If adopted as policy, the council will start a lobbying campaign, to target the Home Office in particular. Local people will also be targeted through PR initiatives.
Corporate communications officer Sam Hart, who handles community safety issues, said: 'It's early days but the panel believes there is already widespread support for such a centre. We have a huge problem in the borough and people are open to new ways to dealing with it.'
The council has lobbied Government before on this issue. Last year it submitted a paper to the Home Office calling for a relaxation of drugs laws to better help addicts get treatment.
Camden is one of Britain's drug-abuse hotspots. It has five times the national average of drug abusers and three main areas where drugs are sold - King's Cross, Camden Town and Camden's part of the West End.
Measures already taken by the council include the creation of drug action response teams to clear up discarded needles and dog warden patrols that target public areas of drug abuse.
Next month it is launching a neighbourhood warden scheme in King's Cross. These wardens will be tasked with, among other crime prevention duties, gathering information for the police.
Similar projects to the proposed injecting centre are already in operation in Rotterdam, Liverpool, New York and Portugal.
The borough's local paper the Camden New Journal refers to the centres as 'Dutch-style shooting galleries'.