Contractors chosen by the city council for the shortlist are: C Spencer, Galliford Try, Kier Northern, Laing O’Rourke, Vinci and Wates.
The bus station forms the first phase of the wider £350m ‘East West’ retail scheme led by Realis Estates.
Shortlisted teams will now undergo the main tender for the works before a successful contractor is selected in the spring.
Realis Estates managing director Duncan Mathieson said: “We are delighted to announce such a strong shortlist of contractors, which includes a number of the biggest names in the industry.
“The project has created a lot of interest so narrowing the shortlist down to just six companies has not been easy.
“We want to make sure we choose the right contractor for a scheme of this size and importance, and so we will spend the next few months carefully reviewing the tenders before making our final decision.”