The crew behind SS Nomadic are considering running a joint ticketing scheme with their neighbours Titanic Belfast.
Almost 1,000 members of the public boarded the Titanic's little sister at the weekend after she opened for the first time after her £7m restoration.
But among those visitors, there were a few complaints about having to buy separate tickets for the historic vessel and then fork out for the neighbouring Titanic Belfast attraction.
"If I was in Paris and there were two such closely linked attractions so near to each other, I wouldn't be very happy that I had to pay for separate tickets," one caller told the Belfast Telegraph.
"It can end up being an expensive day out if you have to pay for both."
But Nomadic Charitable Trust chief executive Dennis Rooney said his team will be in talks with Titanic Belfast in the next few weeks over the prospect of setting up a joint ticketing scheme.
One tourism expert said Northern Ireland doesn't seem to have got over the hurdle of getting tourism operators to co-operate rather than competing with each other. Dr Peter Bolan, director for international travel and tourism management at the university of Ulster, said: "If any attractions were to go well together, it would be Titanic Belfast and SS Nomadic. It would be strange if we didn't go down the route of having joint ticketing there, because there is the obvious connection."
A spokesman for Titanic Belfast said they "look forward to working collaboratively with SS Nomadic to the benefit of all visitors to Titanic Quarter".
SS Nomadic was built at Harland & Wolff and was launched in 1911. She carried first-class passengers on to the Titanic from Cherbourg. After she was retired in the 1960s, she became a floating restaurant on the Seine in Paris but later fell into disrepair in Le Havre.
The Department of Social Development bought her at auction in 2006 following a major media campaign led by the Belfast Telegraph.