Under the proposal, single adults would be turned away from the city's homeless shelters unless they demonstrated that they had no other housing options.
The Department of Homeless Services has delayed implementing the policy until a judge reviews a separate legal challenge by the Legal Aid Society.
According to the Wall Street Journal (http://on.wsj.com/ucsLCr), the council plans to authorize the lawsuit during a meeting Tuesday.
Council Speaker Christine Quinn has denounced the policy as "cruel" and "irresponsible."
The homeless department's commissioner, Seth Diamond, said Monday that the policy is fair.