The car park would replace the current surface level parking which will be lost when the new replacement for Olympia leisure centre is built at Allan Street.
The report explains that it is intended to procure both the new car park and the replacement for Olympia on the adjacent site at the same time.
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City council administration leader, Councillor Kevin Keenan said: "This is an exciting time for Dundee with ongoing record levels of private and public sector investment. This is evident with construction cranes springing up across the city skyline.
"A multi-storey car park at Allan Street would complement the new swimming and leisure centre on the site which has already been approved in principle."
The plan for the new multi-storey includes the infrastructure for a single 7,000 sq ft retail unit on the ground floor which would be completed to coincide with the opening of the new leisure facility.
(GK/JM)
