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Mr Hodgson floated the idea yesterday during a meeting of the local advisory group assisting the rebuild committee.
He also suggested that once surplus to rebuild requirements, the homes could answer Dunedin's future social housing needs.
About 1000 workers are expected to be employed on the estimated $1.6billion project, and Mr Hodgson said careful planning was needed to house those people and their families.
``The Dunedin City Council has a pretty good handle on the changing housing needs of the city, and where some housing redevelopment might take place,'' Mr Hodgson said.
``The new ingredient in the mix is that Dunedin will inevitably host some hundreds of out-of-town workers for several years while the hospital is being built.
``It makes sense to gather available information together and see whether a bit of co-ordination can facilitate an accelerated house-building programme.''
Mr Hodgson ruled out the hospital building houses itself, but said investors - specifically Ngai Tahu - might be interested.
On Monday, Ngai Tahu told the council 10-year plan hearings the iwi wanted to play a significant role in the cultural and financial future of Dunedin and invest in major city projects.
``The next step is to acquaint these folk with what we know about the likely increase in housing demand,'' Mr Hodgson said.
``This is a very large project in a small city, therefore it makes sense to not leave decisions entirely to the market.
``If we do, then the market might simply soak up commercially available accommodation for years, and if that happens we run the risk of damaging our tourism sector because Dunedin will be too full too often.''
In February, the Otago Daily Times reported demand for social housing in Dunedin continued to rise.
There were 218 people on the council's community housing waiting list at the end of December.
Mr Hodgson, who has previously called the hospital rebuild the largest health sector capital project in New Zealand's history, yesterday said it was inevitable people would migrate to Dunedin to work on such a large project.
``We will need to cater not just for families but single workers, who may prefer to live in simpler, cheaper accommodation,'' he said.
``Also, the main contractor will not be known for a long time yet and may be a significant player in such decisions.''
The local advisory group includes representatives from the council, Otago Regional Council, the Southern District Health Board, Ngai Tahu, the NZ Transport Agency and the Ministry of Health.