Ms Gallagher said she was aware that a "reasonably large percentage" of owners wanted to rebuild on the same land once their house was demolished and the land cleaned, and that was "certainly part of our thinking in the design of a demolition program".

"It is going to be very challenging to be able to offer a program that will be everything to everybody, that will meet everybody's needs, noting how different the expectations and the desires of Mr Fluffy homeowners are," she said.

"But we are conscious that there are a couple of areas where we are getting quite a strong response from homeowners - that is, some would like to leave, and some would like to stay and then there's some people who don't want to be bothered with anything at all. And we're trying to design a program that is sensitive to the needs of all of those people."

Owners of the 1000 homes contaminated with Mr Fluffy loose-fill asbestos insulation are waiting for a decision on a mass buy-back and demolition of their homes, in a program that could cost up to $1 billion.

The indication of an option to allow them to rebuild on the same land will come as a relief to many owners, who don't want to leave their neighbourhoods. But many are still worried the buy-back won't leave them with enough money to buy their land back and rebuild to the same standards.

Ms Gallagher has previously pointed to the Government's need to maximise the returns from selling the land to help recoup some of the enormous costs of the buy-back and clean-up.

Ms Gallagher said she would update the ACT Assembly on Thursday, in line with her commitment to give a quarterly update.