A spokesperson for the council said that it had received legal advice that it could recover some of this money. The council fears unless it does so, it might be forced to raise its council tax.
The spokesperson said: "We have been advised that there is the potential for legal action against parties unnamed. We have been advised we have a good case."
Those parties are understood to include Mowlem, which recently lost a Court of Appeal battle against the council over whether a second contractor, Warings, ought to have been permitted on site to take samples of peeling paint. Another firm potentially at risk from legal action is Grimshaw.
Mowlem is understood to be making a counter-claim against the council. If it is successful, the total cost of the spa could rise to more than £30m.
The council commissioned a report into peeling paint in the autumn, which was carried out by STATS, a materials analyst. The report, which was published in January, found five problems with the paint application.