"We would welcome discussions ... on how we can best work together to meet the demand for affordable rental housing in Hamilton," Mr Bignell said.
Pleas from about 60 pensioners to the council to sell to a compassionate buyer prompted the council to move away from selling it to a private group.
The executive director of the Community Support Association Trust, Peter Heaslip, also expressed interest in buying the flats.
He was concerned a private operator would buy at a low price only to make a windfall from it later. The trust didn't own any elderly housing but was set up to help people, he said.
The city council is the biggest landlord of pensioner housing in Hamilton, followed by St Vincent de Paul, Central Baptist Church, Salvation Army, Methodist Church and Abbotsford House.
Housing NZ provides low-cost housing in Waikato aimed at all groups.