The project aims to attract tourists to the site
Belfast City Council may invest £10m of ratepayers' money to ensure the Titanic Quarter goes ahead.
More than two-thirds of the funding has already been secured, but the development is in jeopardy after it failed to secure lottery money.
The race is on to build the tourist attraction in time for the 100th anniversary of the tragedy in 2012.
A final decision on funding will be made by the council within the next two months.
The signature glass fronted building would be twice the size of Belfast's City Hall, featuring exhibitions and rides at an estimated cost of about £90m.
The pledged funding has already come from the government, Titanic Quarter Ltd and Belfast Harbour Commissioners in an attempt to promote the city's maritime history.
There has been some criticism over whether the council should use so much public money to step in and save the project.
Belfast Lord Mayor Jim Rodgers said he "firmly believed" the council should support it.
"The city council must get involved in it, this is a massive project for the whole of Belfast and Northern Ireland it will bring thousands of tourists," he said.
Following a presentation by Titanic Quarter Ltd to the council a few weeks ago, SDLP Councillor Pat McCarthy said some of the councillors wanted to hand over the money "there and then."
"I asked them to exercise a bit of caution," he said.
"I'm not against it, but I'm not for it, convince me.
"I will back it, if it is a robust business plan and it's not going to be an albatross for the city of Belfast."
In a statement the council agreed consideration must be given to the project and that a final decision would be made before June.