The 28 million pound museum in Southampton, from where the liner set sail in 1912 on her maiden voyage, is set to feature a climb-aboard replica of the doomed ship, which hit an iceberg causing the loss of 1523 lives.
The plans received a boost after the Heritage Lottery Fund awarded almost 500,000 pounds in development funding - with the potential for a further 4.5 million pounds towards construction.
However, the council still requires a further 10 million pounds to fund the first phase of works and is currently in talks to raise the cash.
If successful, the city council's Civic Centre will be converted with the main exhibition hall turned into a scene of the dockside in Southampton with the Titanic about to depart.
The story of the disaster and the finding of the wreck will be part of the exhibition.
Also, about 4,000 items from the ship are set to be displayed within galleries.
"This museum will be of international significance and could attract hundreds of thousands of visitors every year," the Telegraph quoted Councillor John Hannides, as saying.
"Southampton was the home of the Titanic so it is only fitting that we tell our story.
"When the ship tragically sank 549 Southampton people lost their lives and hundreds of families in the city were directly affected. The impact was felt right across the world, but nowhere more so than in Southampton.
"We now need to do all we can to see how we can raise the funds to make this happen," he added.