Southampton City Council (SCC) has selected Kier Southern as its preferred contractor to build the city's new £15m Sea City Museum, which is due to open in 2012.
The final appointment of the contractor - part of the Kier Group - is subject to the approval of the council's cabinet at the end of August, with a pre-contractrual agreement now due to be signed.
Forming part of Southampton's wider Cultural Quarter development, Sea City Museum will be housed within a converted Grade II*-listed Magistrates' Court adjoining the city's Civic Centre.
Two permanent galleries will explore the city's status as a 'Gateway to the World' during the last 2,000 years and its relationship with the ill-fated liner RMS Titanic, which claimed 549 local lives.
Southampton's range of archaeological and maritime exhibits are to be put on show at the Wilkinson Eyre Architects-designed attraction, which will also feature space for temporary exhibitions.
The Heritage Lottery Fund has already contributed £4.6m towards the scheme, with work expected to start on site in October. Gifford, Davis Langdon and Urban Salon are also involved with the project.
John Hannides, cabinet member for leisure, culture and heritage at SCC, said: "The appointment of Kier brings us one step closer to the realisation of the Sea City Museum that will showcase Southampton's amazing maritime heritage."
SCC cabinet member for economic development Royston Smith added: "The Sea City Museum will be a great asset to the Cultural Quarter, which will bring together arts, culture and heritage."
Sea City Museum is scheduled to open in 2012, coinciding with the 100th anniversary of the Titanic's sinking.