OceanGate Expeditions said in a brief statement on Monday that it was "mobilising all options" to rescue those on board the vessel.
The US coast guard did not immediately respond to requests for comment.
Media reports said the coast guard has launched search-and-rescue operations.
It was not immediately clear how many people were missing.
The family of British billionaire Hamish Harding said he was on board.
His stepson wrote on Facebook that Harding had "gone missing on submarine" and asked for "thoughts and prayers".
The stepson subsequently removed the post, citing respect for the family's privacy.
Harding himself had posted on Facebook a day earlier that he would be aboard the sub.
There have been no posts from him since.
In a statement, OceanGate said: "We are deeply thankful for the extensive assistance we have received from several government agencies and deep sea companies in our efforts to reestablish contact with the submersible".
The company is currently operating its fifth Titanic "mission" of 2023, according to its website, which had been scheduled to start last week and finish on Thursday.
The expedition, which costs $US250,000 ($A365,100) per person, starts in St John's, Newfoundland before heading out approximately 640km into the Atlantic to the wreckage site, according to OceanGate's website.
In order to visit the wreck, passengers climb inside Titan, a five-person submersible, which takes about two hours to descend to the Titanic.
The British passenger ship famously sunk in 1912 on its maiden voyage after striking an iceberg, killing more than 1500 people.
The story has been immortalised in non-fiction and fiction books as well as the 1997 blockbuster movie Titanic.
