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Dunedin businessman Ian Taylor has speculated in the past the planned Sustainable Futures building could be a base for Otago and international marine scientists.
Mr Cull on Friday described the university as an "interested" party in waterfront plans for the city.
However, pro-vice chancellor for the Division of Sciences Prof Richard Barker said there were no current plans for an aquarium or marine institute at the site.
He did not respond to further questions.
A proposal to cut three academic staff at the university's department of marine science has revealed the department accumulated a deficit of $12million between 2013 and 2018.
Students have launched a petition against the proposal, which is also opposed by the Tertiary Education Union. However, Prof Barker said on Friday the deficit in the department had reached a level of nearly $30,000 per student, which "cannot continue".
"The department's core operating costs have to be met by other departments that also have to cover the department's share of central university costs."
Factors identified behind the deficit, due to reach $4.2million this year, are the large number of staff relative to core income, high costs associated with the department's vessels, and the costs associated with the recently upgraded and underused Portobello Marine Laboratory.
When asked how many other departments used the fleet of boats, Prof Barker said he could only provide information for Polaris II, for which 77% of bookings were from marine science.
"The department of marine science follows a cost-recovery model to cover running and maintenance costs. They have followed a policy of undercharging to try and increase use by other departments."
The Division of Sciences had been actively promoting marine science programmes in schools throughout the country, and through expos and marketing ventures, and was working with the department on a new marketing campaign to bring in students, he said.