Hull councillors say they have run out land in the city to put forward as a legal transit site for travellers.
Unauthorised camps on council-owned land have cost the authority over £56,000 in clean-up and legal costs over the last two years.
But a search for a suitable new legal site for travellers passing through the city has drawn a blank.
Officials spent two years examining possible options without even coming up with a potential shortlist after former cabinet portfolio holder Martin Mancey asked colleagues to come up with ideas for a site.
Now councillors are asking the government to make it a requirement on neighbouring authorities to provide a site when land is in short supply.
They argue Hull's tight boundary and high flood risk issues across most of the city make it impossible to earmark a site.
Speaking at an overview and scrutiny management committee, chairman Councillor Sean Chaytor said one option could be to look at land owned by the city council in the neighbouring East Riding.
"There is land outside of the city which is owned by the city council.
"Some of that might be suitable but, like any other planning issue, it would require an application to be considered by East Riding Council."
He said flood risk issues and the potential for any site to be close to existing residential areas meant looking beyond Hull's boundary might be necessary.
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The committee broadly supported a draft response to a current government consultation on the issue of tackling the problem of unauthorised traveller encampments.
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