Mr Chisholm suggested it was still possible that the Government would cancel part of the debt even if only part of the city's housing stock is transferred out of council control.
Council chiefs are still considering their options after tenants voted last year to reject their plans to transfer all 24,000 council houses to a new housing association, which would have meant the Treasury cancelling the Capital's entire housing debt.
One of the options is that smaller numbers of council housing would be transferred over a period of time. Mr Chisholm said the idea of a partial debt write-off in return for a smaller-scale stock transfer was "one possible scenario".
He made the comment after Edinburgh Pentlands Tory MSP David McLetchie spoke out in the Scottish Parliament about the need for a "Plan B" to deal with the city's housing needs.
Mr McLetchie asked: "Given that a total debt write-off by the Treasury was a feature of the original proposal for a total stock transfer, would there be a partial and proportionate debt write-off if there were a number of partial stock transfers?"
Mr Chisholm said it was up to the council to look at the options. But he added: "David McLetchie raises one possible scenario."
And he said since 2004 some local authorities had been able to get debts cancelled for the section of their housing stock they transferred to community ownership.
"So that is certainly one of the scenarios that Edinburgh may well be considering," he added.
City housing leader Sheila Gilmore confirmed partial stock transfer was one of the options on the table. She said up until now any small-scale stock transfers have led to five years' debt relief rather than outright cancellation.
But that meant the debt then returned to the council when there were fewer tenants among whom to spread the burden. She said: "We have had some discussions with the Executive about this. In the past partial transfers did not carry full debt write-off.
"They have indicated to us there is possibility that if the overall package looks right, they would now consider that."
She said if a partial stock transfer were to bring about relief from some of the huge debt it would "certainly make it a more attractive option than in the past".
Cllr Gilmore said it was impossible to estimate how much debt might be written off since the level of debt per council house varied widely across the city.
Mr McLetchie said one way forward would be for the council to identify estates suitable for a partial stock transfer to new community-based housing associations.
He said: "Following the council's failure to win approval for the transfer of all its housing stock in last December's ballot, it is essential that we devise a Plan B in order to promote good quality affordable housing in the city.
"One of the features of the total transfer plan was that the Treasury had agreed to write off all the city's accumulated housing debt. If partial stock transfers to community-based housing associations are to work then there will have to be a proportionate and partial debt write-off." He said he was pleased at Mr Chisholm's response.
"He indicated that partial debt write-offs had taken place in the past and I hope that this avenue will be fully explored by the council in its discussions with the Scottish Executive. This is a crucial issue. There is no point in the council simply licking its wounds.
"We need to make progress on affordable housing for the city as soon as possible."