The three options include selling all 377 housing units, keeping all units or keeping most of the units and selling some.
The council estimates a $2.2 million annual shortfall if the status quo is maintained.
Under the plan to keep most of the housing, the council would retain its eight 'retirement' villages, develop 45 more units and sell three 'social villages' leading to a $2.3 million annual shortfall.
The options that produce a shortfall could potentially be covered by a rates increase if they are chosen.
There are currently 12 housing 'villages' run by the council across the city.
The council's preference in the case of any sale would be to sell to another community housing provider with a guarantee of the current tenants existing lease agreements.
The council has not yet identified its preferred option of the three.
Napier Mayor Kirsten Wise said it is important to know what council housing tenants and ratepayers think of the three potential options.
"Ensuring low-income and vulnerable residents have affordable housing is very important. Potentially changing our housing provision arrangements is a significant decision and we want to know what people think before we make that decision."
"Tenant welfare is very important to us. It's also important that we balance the needs of our tenants with the wider impact council's housing provision has on our ratepayers."
Of the 377 council-owned units, 80 per cent are for retirees or people with a disability.
The consultation closes April 20 and the council will consider submissions at a meeting on May 18.
The council has received 52 submissions so far, with 45 coming in on the first day.
Submissions can be made online at www.sayitnapier.nz or in hard copy forms available along with information at the Napier City Council Customer Service Centre, Taradale Library and Napier Library.
Completed hard copy submissions can be dropped in to the Customer Service Centre or posted in using the Freepost facility.