The 48-year-old venue on Ryndle Crescent has stood empty for four years following the opening of Scarborough Sports Village, which is now home to a new pool, gym and Scarborough Athletic Football Club.
Councillors will be asked to progress the demolition plans at a meeting next Thursday when details of the works will be set out.
This will involve the removal of asbestos from the building, as well as the demolition of foundations and the pool structure.
A report to the meeting said the pool had become "unkempt" since it fell into disuse and that it is not considered to be of any "architectural or townscape merit".
The plans are part of a wider regeneration scheme for Scarborough’s North Bay, known as the Sands development.
This involves hoardings to be placed around the former Atlantis water park which had been earmarked to become a multiplex cinema before the plans collapsed earlier this year.
Toilets at the Northstead Upper car park will also be refurbished as part of the scheme.