Speaking at a news briefing, Mr Cuomo said PANYNJ senior staffers would be tested and 'several of them may be on quarantine'.
A PANYNJ public information officer, Lenis Rodrigues, said Mr Cotton 'is currently asymptomatic and has self-quarantined at his home while maintaining a full schedule.'
Ms Rodrigues said some PANYNJ staffers are working remotely as a precautionary measure.
'Any staff members who have had close contact with him in recent days are also working from home as they follow the guidelines and protocols put in place by the New York State Department of Health,' she said.
In addition to the Port of New York and New Jersey, PANYNJ is responsible for area rail, bridges and tunnels, as well as John F Kennedy International, LaGuardia, Newark Liberty International, Stewart International and Teterboro airports, reports American Shipper.
Mr Cuomo said Mr Cotton had been overseeing the arrival of international flights at area airports, including JFK. 'He has been at the airports obviously when many people were coming back with the virus,' the governor said.
Mr Cotton was named executive director of the bistate port authority in August 2017. He previously served as Mr Cuomo's special counsellor for interagency initiatives, serving as the point person for major infrastructure projects. Before that, he was the general counsel for NBCUniversal.
Mr Cuomo said at the time: 'With major infrastructure projects across the region underway, including the new JFK and LaGuardia airports, the port authority has unprecedented momentum, and Mr Cotton has the experience and tenacity to continue moving these transformative projects ahead and lead the organisation into the future.'