Cumbria County Council lodged a bid to buy the library on Milbourne Street in the summer but has since pulled out.
A spokeswoman for Cumbria County Council said: “The council has decided not to purchase this property after assessing the business case for a purchase.”
The cash-strapped authority is already building a new £10.4m purpose-built headquarters in Botchergate which will cater for up to 700 civil servants and will see the authority leave its Citadel base.
The former university library building, which stands next to Caldew Bridge near the city centre, was first built as a learning resource centre in 2002 and cost more than £3m. It was originally part of the University of Northumbria’s Carlisle campus and was later taken over when the University of Cumbria came into being in 2007.
It is being marketed by Edwin Thompson.
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