The plan was revealed by cabinet member for housing Cllr John Wright (Con) during the full council meeting last week.
It was prompted by a follow-up question from Cllr Mike Henderson (Lib Dem), who was not happy with the tabled response.
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He had asked what action Cllr Wright was taking to provide temporary housing for homeless people in the Faversham area so they are not pushed away to Medway, severing connections to their local community.
The answer given was that “housing services is working hard to ensure this only happens in situations where it is absolutely necessary and for as short a time as possible”.
However, Cllr Henderson said he felt it only explained what the officers had been doing.
Cllr Wright said: “We have been focusing on trying to prevent homelessness, so it’s about having that advice to people to try and prevent [them] becoming homeless in the first place, and the council has been fairly successful in doing that.
“For those people that do find themselves homeless, there is the issue around temporary accommodation for them to use, and there are occasions we have to use B&Bs in Medway and Canterbury and outside of Swale.
“There are B&Bs in Swale and, yes, we do use them, and we try to keep those stays as short as possible and find them accommodation as quickly as possible.
“In terms of ideas to stop or try and prevent people going out of the borough, officers are working on a business case where the council might invest in its own B&B to alleviate some of the problems it currently has – but that needs to be worked up and it does need to come to cabinet for approval.”
After the meeting, Cllr Henderson said: “Nobody had said anything, so it was news to me and the majority of councillors.
"He didn’t specify it would be in Faversham. I would make a small bet it will be in Sittingbourne.”
A Swale council spokesman said: “Yes, we are looking at a proposal to establish housing to be used as emergency temporary accommodation, but this is at very early stages and therefore there are no further details available at this time.”