Gov. Andrew Cuomo is speaking with his counterparts in New Jersey and Connecticut about people traveling from states with coronavirus cases that are increasing out of concern the virus could once again spike in the northeast, he told CNN in an interview on Monday.

Cuomo has not ruled out a potential quarantine for people traveling into New York from states like Florida and Texas as the infection rates there continue to increase. In New York, testing has shown an infection rate daily of less than 1 percent over the last several days.

"The greatest irony when they write the book in history, New York had the highest infection rate and all these other states were saying, 'well, we're going to blockade New York,' " Cuomo said. "The president was talking about blockading New York."

Cuomo said he would not want to target a "specific state" for a quarantine, but is speaking with Phil Murphy in New Jersey and Ned Lamont of Connecticut about the issue.

"I would consider states with the highest transmission rate that, if somebody comes from that state to New York, there's a period of quarantine where they quarantine themselves to make sure they are not spreading it," he said.