Passengers can get off the ship there if they want, according to the report, or wait until the port reopens on the cruise. The storm also forced the U.S. Coast Guard to close multiple ports along Texas Gulf Coast, including those at Houston, Galveston, Texas City, Freeport and Corpus Christi.
The company said the Carnival Freedom and Carnival Valor, which were scheduled to return to port on Saturday, would "remain a safe distance from the storm" on Friday. The ship was expected to leave Cozumel for Galveston Saturday afternoon, and Dessin said she wasn't sure if she'd make her flight back home to New Jersey.
The other ship, the Carnival Breeze, was slated to return to the port on Sunday, but remains at a dock in Cozumel, Mexico.
The Port of Galveston shut down at noon on Friday in preparation for Harvey, which eventually made landfall as a category 4 hurricane.
The Freedom and Valor's next cruises will be on a shortened itinerary that will be determined in the next few days, officials said. "We are strongly encouraging them to remain on board as we intend to return the ships to Galveston as soon as feasible".
Carnival and Royal Caribbean cruise lines are both monitoring the storm to figure out the best course of action between now and the weekend.
Casey Stegall was reporting live from Galveston, Texas, for Fox News, when his broadcast was interrupted by a woman handing him some cans of beer.
Guests who wish to cancel their cruise may do so without penalty and receive a future cruise credit.
Royal Caribbean said its Texas-based ship, Liberty of the Seas will stay safely behind the storm for now.