The council has heard previously that Santia spent six weeks at the site but only located 10 per cent of the asbestos subsequently found but it has said all asbestos found in the building has now been removed.
This means the project costs have significantly increased from the original estimates - from £1.18 million to £4.1 million, including fees.
Councillor Rob Stewart, Swansea Council Leader, said: "The original scope of works were to be covered by the Welsh Government via their Vibrant and Viable Places Swansea City Centre Regeneration Programme, but the failure of the original asbestos survey to identify the amount of asbestos in the building means the project costs have greatly increased.
"As a council, we have followed all due diligence throughout this project, so we're looking to recover a proportion of the additional Oceana costs from Santia. We're also in the process of securing further investment from the Welsh Government and via the City Deal, which we hope to sign in coming months.
"Subject to funding, the Oceana building will be replaced with a new office development on site that will form part of an employment district we're planning for Kingsway. This overall scheme won't just generate income to protect council services for residents across Swansea – it will also create high-quality office accommodation for new businesses to accompany. This will help keep jobs in Swansea and create many more."
Read more at