British Health Secretary Steve Barclay has said he "does not recognise" a report that the government wants to move towards a Swiss-style relationship with the EU.
Under the new Prime Minister Rishi Sunak, the UK will pursue frictionless trade with the EU in a deal modelled on Switzerland's relationship with the bloc, although this would not involve a return to freedom of movement, The Sunday Times reported.
Any such shift, not long after former prime minister Boris Johnson secured a deal with the EU after years of back-and-forth negotiations, would likely inflame backbench Tory Brexiteers.
"I don't recognise this story at all," Mr Barclay told Sky News on Sunday. "I don't support that. I want to maximise the opportunities that Brexit offers."
Switzerland has negotiated access to the European single market, but in return has to accept conditions including allowing freedom movement of workers from EU countries and payments into the bloc's budget.
Simon Clarke, a former minister, was among those to criticise any suggestion that Britain could pursue a Swiss-style deal.
"I very much hope and believe this isn’t something under consideration," he said on Twitter.
"We settled the question of leaving the European Union, definitively, in 2019."
Britain is currently locked in talks with the EU over the Northern Ireland Protocol. This is the part of the Brexit deal that mandated checks on some goods moving to Northern Ireland from the rest of the UK due to the region's open land border with EU member Ireland.
Unionists have opposed the protocol, claiming it impedes trade between Northern Ireland and Great Britain by placing a border in the Irish Sea.
This has resulted in the collapse of Northern Ireland's devolved government, with senior civil servants left to run departments.
However, there have been renewed hopes in recent weeks that a deal can be secured and the relationship improved between the UK and the EU after years of tension.
Agencies contributed to this report