New York Gov. Andrew Cuomo is instructing hospitals across the state to test specifically for the variant of the coronavirus discovered in the United Kingdom.

“If we find the variant, we want to know where it is immediately,” Cuomo said. 

Cuomo said he does not support a travel ban from the U.K. into the U.S., but does believe the U.S. should follow New York state’s lead in requiring flights originating in the U.K. to have passengers test negative.

Dr. Anthony Fauci told ABC News’ “Good Morning America” Tuesday that “the possibility and maybe the likelihood of requiring the testing of individuals before they board a plane to the United States -- that is under active discussion.”

Fauci added, “you really need to assume” that the variant is already in the U.S.

ABC News’ Aaron Katersky contributed to this report.

South Carolina Gov. Henry McMaster has tested positive for COVID-19 and is experiencing “mild symptoms with a cough and slight fatigue,” his office said.

His wife, Peggy McMaster, tested positive last week and does not have symptoms.

"There is no way to pinpoint precisely when or how Governor McMaster or the First Lady contracted the virus,” the governor’s office said, citing state physicians.

“The governor quarantined himself when he knew he was in close contact with the virus and sent Governor’s Residence staff home to quarantine and get tested to ensure their health and safety,” his office said. “Because the governor followed the guidelines and recommendations as a ‘close contact,’ SCDHEC [the state’s health department] has determined there are no ‘close contacts’ to the governor."

The governor is isolating at home and will receive monoclonal antibody treatment on Tuesday, his office said.

The Centers for Disease Control and Prevention said it hasn’t detected the coronavirus variant found in the United Kingdom, with the caveat that an extremely limited number of COVID-19 cases in the U.S. have been sequenced.  

While there’s evidence the variant could potentially be more transmissible, the fact that it is more predominant in a particular country or area doesn't mean it's more infectious and there's no evidence it causes more severe illness, according to the CDC.

Beginning in January, each state will send at least 10 COVID-19 samples biweekly to the CDC for sequencing and further characterization. 

ABC News' Stephanie Ebbs contributed to this report.

With over 51,000 coronavirus-related deaths recorded in the first three weeks of the month, December is on track to surpass April to become the deadliest month of the pandemic in the U.S., according to ABC News’ analysis of data compiled by the COVID Tracking Project.

Hospitalizations are surging to unprecedented levels, with 115,351 patients currently hospitalized nationwide -- a 38.5% increase in the last month.

December is also set to become the worst month on record for COVID-19 cases in the U.S. The U.S. surpassed 18 million cases on Monday, only four days after reaching 17 million cases, according to data collected by Johns Hopkins University. 

ABC News’ Arielle Mitropoulos contributed to this report.