The building maintenance workers union, 32BJ SEIU, which has 175,000 members nationwide, has also been in contact with the state, a spokeswoman said.
Con Edison has already received assurances from state officials that its approximately 4,000 to 5,000 critical customer contact workers will be prioritized.
Tony Utano, president of Local 100 of the Transportation Workers Union, which represents 40,000 city bus and metro workers, said he spoke with Patrick J. Foye, the chairman of the Metropolitan Transportation Authority who is nominated by Mr. Cuomo, for the inclusion of its members, and expected them to be included in the next round.
An advisory committee from the Centers for Disease Control and Prevention has previously reported that it could include a large portion of the U.S. population: around 87 million essential workers, including police, firefighters, teachers, farm workers, laborers public transport and others.
The CDC is expected to publish its guidance soon.
In the meantime, companies and groups across the country have explained to the federal agency why they should be part of the next wave of vaccinations.
Farm workers, from rice farmers to pig farmers, fought for priority, as did trade associations representing school nurses, truck drivers, firefighters and even zookeepers.