The council's development committee has written to Environment Minister Alex Attwood to stress the need for movement, 10 months after the planning application was submitted by the university's authorities.
Work on the planned revamp of the York Street campus was scheduled to get under way in late spring or early summer. But that timescale could be impacted if the planning process drags on.
The five-year building project is predicted to sustain thousands of construction jobs.
When the application was submitted, Mr Attwood said such major planning decisions should ideally be made within a six-month timescale.
The council committee agreed to write to the minister after receiving a presentation from the university.
Committee chair Alderman Christopher Stalford said: "The committee was unanimous in the view that the proposed development at York Street would act as a catalyst for the regeneration of the city."
He added: "However, the committee also expressed concern about the time being taken to process the planning application which had been submitted by the university.
"Given the importance of the development to the city, members expressed a desire that the application for the development be considered by the council's town planning committee on March 7.
"The development committee agreed that a letter should be written to the minister setting out the council's concerns and requesting that the issues outstanding regarding the application be resolved at the earliest opportunity, to enable the development to be approved."