The newspaper reported on its website that Democratic Governor Andrew Cuomo -- a long-time opponent of legalizing medical marijuana -- was planning to announce the new guideline next week in an executive action.
The decision would see New York mirror a growing list of states which have taken an increasingly progressive stance on marijuana use. Colorado this week became the first US state to legalize the drug for recreational use.
The Times reported that New York's new policy would be far stricter than in California, which has already loosened its rules on medical marijuana.
In California, people suffering from mild ailments can obtain prescriptions for the drug; in New York it will be made available in only 20 designated hospitals across the state for individuals suffering from cancer, glaucoma or other diseases.
New York retains some of the most draconian sanctions of any US state for individuals caught dealing or using drugs.
However Cuomo's apparent policy U-turn would inch it closer to the softer policies that are rapidly gaining traction in the United States.
Saturday's report said New York hoped to have the infrastructure for dispensing medical marijuana installed later this year.
The move comes amid a nationwide campaign to relax laws on marijuana use which has been buoyed by shifting attitudes on the drug.
In October, for the first time in a Gallup poll, a majority of Americans -- 58 percent -- said they favored the legalization of marijuana.