The Mail on Sunday newspaper reported: "Lord Frost tendered his resignation a week ago - but was persuaded to stay until January". Express.co.uk has contacted Number 10 for comment.
If the reports are accurate, Lord Frost's decision will pile more pressure on the Prime Minister at a time when he is reeling from the Tories' disastrous loss in the North Shropshire by-election, and the worsening Covid-19 situation as cases rocket, fuelled by the Omicron variant.
Lord Frost's most recently public remarks came yesterday, when he tweeted: "I have spoken to @MarosSefcovic today and I have now issued a statement on the state of play in the talks on the Northern Ireland Protocol.
"The negotiations will resume early in the New Year."
Lord Frost, a staunch advocate of Brexit, has spearheaded attempts by London to re-open negotiations over the terms of Britain's exit from the European Union.
His decision was reportedly driven by plans to introduce Plan B Covid measures, including vaccine passports.
Lord Frost has recently been locked in tense rounds of talks with European Commission vice-president Mr Sefcovic as the UK and the EU attempt to close gaps in post-Brexit arrangements.
READ MORE: Brexit LIVE - 'Disillusioned' Frost quit No10 cabinet as 'Covid Plan B' the final straw
Labour's deputy leader Angela Rayner wasted little time rubbing salt in the wound, claiming the news represented "a Government in total chaos right when the country faces an uncertain few weeks".
She tweeted: "BorisJohnson isn't up to the job. We deserve better than this buffoonery."
Liberal Democrat foreign affairs spokesperson Layla Moran said: "This shock resignation is a sign of the chaos and confusion at the heart of this Conservative government.
"The rats are fleeing Boris Johnson's sinking ship as he lurches from crisis to crisis.
"Even the Prime Minister's once-loyal supporters are now abandoning him, just as lifelong Conservative voters are switching in their droves to the Liberal Democrats.
"At a time we need strong leadership to get us through the pandemic, we instead have a weak Prime Minister who has lost the support of his allies and the trust of the British people."
Meanwhile Northern Ireland's former first minister Arlene Foster described Lord Frost's resignation as "enormous".
In a tweet, she said: "The resignation of Lord Frost from the Cabinet is a big moment for the Government.
"But enormous for those of us who believed he would deliver for NI."
(More to follow)