The centre, which was previously student accommodation, was built in 2019 and has stood vacant since 2020, the Local Democracy Reporting Service (LDRS) said.
The council previously said the flats would help offer temporary accommodation for single people and couples who are homeless or at risk of homelessness.
However, the council needs a certificate from the Building Safety Regulator (BSR) before it can start work to bring the site up to standard.
Green Party city councillor Patrick Kitterick told the BBC: “I have huge concerns about that building because the council spent £11m on it a year ago and it still can’t give any indication of when it might open.
“It’s taken them months even to apply for a certificate so they can use it and there’s no guarantee it will be granted.
“Every month this continues it’s costing taxpayers more than £10,000 to keep it secure.”
The council said it applied for the certificate on 8 May.