LONDON -- British Prime Minister Theresa May and her Brexit secretary David Davis are embroiled in a stand-off over a proposed deal to keep Britain linked to the European Customs Union after Brexit, local media reported Thursday.

Davis was in "open rebellion" and refused to be the frontman for the PM's plans of a customs "backstop" to avoid a hard border between Northern Ireland and the Irish Republic, The Daily Telegraph reported.

Davis's revolt came after May refused his demand to define a precise time limit for the backstop solution, according to newspaper The Sun.

The proposal has been put forward as a fall-back solution if no other arrangement is reached to avoid a hard border in Northern Ireland, but the cabinet is divided over whether it should include a specific time limit.

So-called Brexiteers warned that without a fixed end date, the "temporary" arrangement could continue indefinitely.

Some seasoned political commentators suggested that the rift could lead to Davis resigning just days before the critical voting on May's crucial Brexit Withdrawal bill in the House of Commons.

The Brexit secretary is considering resigning if the Customs Union proposal is published without his approval, according to media reports.

When Britain leaves the European Union (EU) next March, the 500-kilometer border between Northern Ireland and Ireland will become the only EU frontier with Britain.

Both British and Irish governments have insisted there should be no hard border.

In a sign of growing concern among Conservative Eurosceptics over Downing Street's Brexit plans, David Jones, a former Brexit minister, has told the PM she must keep Davis on side, The Independent reported.