Josh Blank suffered burns over more than 70 percent of his body after a woman, Rhonda Kavee, doused the grill with alcohol in an attempt get a fire started, The New York Daily News reported Monday.
The boy was reported in critical but stable condition at New York-Presbyterian Hospital Weill Cornell.
Kavee was having a birthday party for son at her Manhattan dental office and was trying to light a grill so the children could toast marshmallows, investigators said.
Police said heavy rains had forced the planned cookout indoors.
A source told the newspaper police considered the incident an accident but were working with the Manhattan district attorney's office to determine if any charges are warranted.
Members of Congress to keep receiving porn magazine
Rosie O'Donnell unveils nearly 50-pound weight loss