The chosen team will support client Associated British Ports' submission to a public inquiry into the scheme, which is due to start on 27 November. Bidders said they expected to hear who had won the contract in time for the start of the inquiry.
Construction will start in 2003 if ABP is successful in the planning inquiry, which is expected to last for a year.
If approved, the container port would be built in Dibden Bay, west of the present port, where it would form an extension to the existing Southampton Water scheme.
The scheme is opposed by environment groups, who claim that the construction and operation of one of the largest dock areas in Europe would blight a large area of the New Forest national park.
Groups such as the Environment Agency and Friends of the Earth say the port would affect five sites of special scientific interest.
Environmental groups claim the port will be damaging to the New Forest and sites of special scientific interest
Residents have also raised concern over the increase in container-related traffic during and after construction.
ABP claims the scheme is required to meet an urgent need for more space – the port handles more than 6% of the UK's shipping trade with the rest of the world.
The project will have major infrastructure elements, including rail and road links, and will create a freshwater lagoon.
ABP revealed the plans for the Dibden terminal in 1997 although a formal application was not lodged until October last year. ABP says a port would create 3000 jobs.
Southampton council also supports the scheme. A spokesman said: "Having completed a detailed examination of the evidence it is clear that the continued economic prosperity of the city and the city region depends on a thriving, growing port.