Properties could be warmed by one or more facilities that extract heat from air, water or underground.
Biomass, hydrogen and systems that draw thermal energy from warm water that households flush down drains could also be used.
Many of the properties are currently heated by mains gas.
Current estimated costs of a heat network in Inverness range from £30m to £54m.
One of the proposed zones, the west bank of the River Ness has a "high level" of social housing and risk of fuel poverty, according to a report discussed by councillors this week.
It also contains buildings with high heating demands, including Highland Council's headquarters, Eden Court arts venue, Inverness Leisure swimming pool complex and the city's botanic gardens.
Another of the buildings, Inverness Ice Centre, has been struggling with its energy costs.
Council officers said the area could benefit from a heat network.
They said an energy centre could potentially be built on council-owned land near Highland Rugby Club's stadium.
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