People in the borough have only been able to use the tip in Stourbridge since the start of April after an agreement with Wolverhampton Council for Bilston's Anchor Lane tip broke down after a finance row.
Dudley Council leader Patrick Harley had thrashed out a deal for Dudley residents to use the Shidas Lane tip in Oldbury, but Sandwell Council pulled out.
Now Councillor Harley says a new agreement with an unnamed neighbouring council was "very close".
He said the new plan would see residents in that council area able to use the Stourbridge tip under a "shared agreement".
Councillor Harley said: "We're confident that we will have a deal with a neighbouring authority very shortly. We are very close. It will benefit not only our residents but their residents as well.
"So there will be a shared agreement where we can use their tip and they can use the one in Stourbridge. It will be very controlled.
"The other neighbouring authority's cabinet has got to meet to finalise it, but without the pressure of local elections I'm sure we will have an arrangement in place very soon."
A political row broke out over the use of the Anchor Lane site in the run up to the elections. Labour-run Wolverhampton Council wanted to increase Dudley's fee by 66 per cent to more than £330,000.
Conservative-run Dudley Council described the increase as "extortionate" and refused to pay, meaning residents in the borough were left with access to only one tip.
The deal for Anchor Lane was initially agreed in 2003, with the increased charge of £200,000-a-year coming into effect in 2008.
Wolverhampton Council argued that the increased charge was fair given the high usage levels of the tip by Dudley residents.