Edinburgh City Council's regulatory committee will consider, on Monday, removing them from the list that require a public entertainment licence.
The move comes after a series of raids by Police Scotland last year in which officers, along with social workers and health and safety investigators, mounted an apparent push against claims of so-called accepted prostitution.
The council has said that its current policy, which has been followed for 30 years, has not been achieving its aim of harm reduction and is no longer sustainable.
Councillor Gavin Barrie, Convener of the Regulatory Committee, said: "Recent checks on licensed premises have uncovered evidence that activity beyond the terms of the licence is taking place in some premises. The proposal to be considered states that the amount of evidence we have now received means it is no longer appropriate to consider saunas and massage premises for a public entertainment licence.
"If the Committee decides not to license these premises in future, the council will still take the safety and wellbeing of those working in saunas and massage premises extremely seriously and our Health, Social Care and Housing Committee will scrutinise the harm reduction work under way across the various agencies."