The council said the baths - which date back to 1905 - will be given a "new lease of life" and "remain a city landmark" under the proposed sale which was announced last year.
An unnamed private developer was lined up to buy the Grade II listed building, but the sale was put on hold for six months after Ripon City Council successfully nominated the baths as an asset of community value.
This protected status meant any community bids could come forward.
However, the borough council has confirmed none were received and that it was now pushing ahead with the sale as previously planned.
A council spokesperson said: “Following Ripon Spa Baths being listed as an asset of community value and the relevant moratorium periods initiated and concluded, we received no further bids for the purchase of the property.
"The generation of funds from assets that are no longer needed allows significant investment to be made in new facilities, such as the new pool in Ripon, the redevelopment of the Hydro in Harrogate and the new leisure and wellness centre in Knaresborough.
"Due to the sale of the baths being ongoing, the details of the preferred bidder are confidential.”
Although Ripon City Council nominated the baths as an asset of community value, it did not make a bid to buy the building.
This is because it believes the city should be gifted the baths which had previously been under the control of the Ripon borough until 1974 when Harrogate Borough Council was created.
Councillor Andrew Williams, leader of Ripon City Council, said: "We believe the building should come under the control of the city council, particularly given the fact that Harrogate Borough Council will soon cease to exist.
"We hope the borough council will revisit this issue and realise that in its dying embers, it would be far better to look at the long term benefits to the community rather than simply trying to raise a few quid on a flash sale."
Councillor Williams also said the city council wanted to take over Ripon Town Hall, Hugh Ripley Hall and the city's market square ahead of Harrogate Borough Council being replaced by the new North Yorkshire Council from April 2023.
Councillor Williams added: "All of these assets will be best managed and maintained with the body that has got the most interest in doing that - and that is the city council."
Ripon Spa Baths was the last of its kind to be built in England and was officially opened by Princess Henry of Battenberg 117 years ago.
The building was previously put up for sale by the borough council in 2008 with a reported £3.3 million price tag, but it was later taken off the market after a community campaign.
It is now up for sale again for an unknown asking price as a new swimming pool has opened at Ripon's newly-named Jack Laugher Leisure and Wellness Centre.
The new pool opened after months of costly delays on 2 March and refurbishment works on the adjoining leisure centre are still underway after the discovery of an underground void prompted the need for an ongoing investigation.
By Jacob Webster, Local Democracy Reporter