“We’d like to see [it] quarantined because it’s a hotspot,” he told reporters. “I’m thinking about that.”
He spoke as confirmed cases in the state increased to more than 52,000, with at least 728 deaths.
But the state’s governor, Andrew Cuomo, said he had not discussed such measures with the president.
“I didn’t speak to him about any quarantine,” he told reporters shortly after he held a call with Mr Trump.
“I haven’t had those conversations,” he added. “I don’t even know what that means.”
New York state has the highest number of cases of Covid-19 in the US.
Mr Trump also said “New Jersey [and] certain parts of Connecticut” could be quarantined under the new measures.
“We might not have to do it but there’s a possibility that sometime today we’ll do a quarantine — short term [for] two weeks,” he said.