The Welsh Health Secretary is to write to his Westminster counterpart about "inflammatory and untrue" comments by the Countess of Chester Hospital's chairman.
Chairman Sir Duncan Nichol said the hospital was "not being paid" for all its work by NHS Wales.
He said that meant it was "hard to countenance" treating Welsh patients.
The Welsh government said its patients were funded in line with the pricing rules set by the NHS in England.
A spokesman said Health Secretary Vaughan Gething would write to UK Health Secretary Matt Hancock "expressing his concern at the messages being given by a senior official in the English NHS".
"The allegations made by the chair of the Countess of Chester Hospital NHS Foundation Trust regarding Wales not paying for its activity are inflammatory and untrue," he said.
"This hospital relies heavily on patients from Wales and the statements made by the chair are not in the best interests of partnership working across the Wales-England border."
Sir Duncan said the hospital needed to "win" arguments about funding with Wales otherwise "we will continue to run our hospital safely but not be paid for it".
Funding from the NHS in Wales makes up 11% of the income for the Countess of Chester Hospital NHS Trust, while Betsi Cadwaladr University Health Board, which funds North Wales patients treated in Chester, is the second largest funding provider to the hospital.
The health board said it paid the hospital for its healthcare in the same way as it does other English health providers.
The Chester hospital has forecast its accounts will be in deficit by £12.7m by April 2019.