The owner of the vessel, which was built for the 1962 movie Mutiny on the Bounty with Marlon Brando and has also featured in Pirates of the Caribbean with Johnny Depp, said he lost contact with the crew late on Sunday.
The US Coast Guard command center in Portsmouth subsequently received a distress signal, confirming that the ship was in distress and locating its position.
"The vessel was reportedly taking on water and was without propulsion," the statement said, noting that weather at the scene consisted of 40 miles-per-hour (65 kilometers-per-hour) winds and 18-foot (five meter) waves.
The current HMS Bounty is a replica of the eponymous British vessel known for the mutiny that took place in Tahiti in 1789.
The Coast Guard's latest statement said they were monitoring the situation to "determine the soonest" time that aircraft or boats can be deployed to make a rescue.