Prime Minister Boris Johnson is expected to set out his decision later on the findings of an inquiry into the conduct of Home Secretary Priti Patel.
Sources familiar with the Cabinet Office report told the BBC it concluded Ms Patel broke rules on ministers’ behaviour.
She has always strongly denied allegations of bullying.
Labour has written to the standards committee calling for a fresh investigation.
The party’s shadow home secretary, Nick Thomas-Symonds, said the prime minister appeared to be involved in a “cover-up” and called for the full report to be published.
He told BBC Breakfast: “This has all the hallmarks of a prime ministerial cover-up and raises serious questions about his judgment.
Mr Thomas-Symonds added: “If these revelations are correct, it is tantamount to condoning bullying, and in no other workplace would this be acceptable. It smacks of one rule for the government and one rule for everyone else.
“We need to see the report in full and the home secretary and the prime minister need to come to Parliament to answer these very serious questions.”
Normally if a minister breaches the code they are expected to resign. But a number of Tory MPs have rallied to Ms Patel’s side, describing her as a determined person doing a tough job.
Health Secretary Matt Hancock told the BBC she was an “excellent home secretary” who had “been nothing but courteous and kind in all the dealings I’ve had with her”.
Mr Johnson has backed Ms Patel so far and there is little sign that will change.
The inquiry was launched after Home Office boss Sir Philip Rutnam resigned in February.
Sir Philip – who is suing for constructive dismissal – alleged staff felt that Ms Patel had “created fear”.
The report, carried out by the government’s independent adviser on standards, Sir Alex Allan, has not been published.
But one source said it had concluded that the “home secretary had not met the requirements of the ministerial code to treat civil servants with consideration and respect”.
They added that the investigation had found evidence of bullying, even if it had not been intentional.
Another source who saw the report called it “unambiguous in stating that Priti Patel broke the ministerial code and that the prime minister buried it”.
A spokesman for the home secretary said she had always denied the allegations and that there had never been any formal complaints made against her.
It’s a government document setting out “expected standards” of behaviour in office, which include “consideration and respect” for civil servants and other colleagues.
The code says “harassing, bullying or other inappropriate or discriminating behaviour” will not be tolerated.
It adds that ministers are “personally responsible” for how they act – and that they can stay in office “for so long as they retain the confidence of the prime minister”.
The code is not legally binding but, according to the Institute for Government think tank, there is growing pressure for it to become so.
A different government source has suggested that the report also paints an unflattering picture of how Ms Patel was sometimes treated.
The report is understood to have looked at Ms Patel’s behaviour at three different government departments – the Home Office, Work and Pensions and International Development.
The evidence gathering was completed several months ago, but Downing Street has delayed giving a decision on the findings.
The prime minister is the ultimate arbiter of the ministerial code, and there is no requirement on the government to publish Sir Alex’s report.
The BBC understands there have been conversations in government this week about how to manage the situation, with suggestions that Ms Patel may be given a reprimand, or be asked to apologise, but keep her job.
Earlier this week former Cabinet Secretary Sir Mark Sedwill suggested there could be a “wider range of sanctions”, telling MPs: “I don’t think it should be binary between let off or sacked.”
He confirmed then that the report was already “with” Mr Johnson.
Dave Penman, general secretary of the FDA senior civil servants’ union, said “thousands” of civil servants would be asking what “message” it would send if the government suggested Ms Patel did not have to resign over a “little bit of bullying”.
He described the system as not “fit for purpose”, adding: “We need an independent process that’s not relying upon a prime minister making a political judgement rather than judging based on the evidence.”
But several Conservative MPs have offered Ms Patel their support.
Tom Tugendhat tweeted that she was popular “across” the party because she was “hardworking, determined and has been very kind to many”.
Another Tory MP, Julie Marson, said the home secretary was doing a “huge job”, adding: “Like many women operating in a man’s world, you have to be strong and decisive.”