Home Secretary Priti Patel broke rules on ministers’ behaviour, according to a draft report, it was claimed today.
The Cabinet Minister, 48, has always denied claims of bullying and her spokesman said there have never been formal complaints against her.
But a draft investigation completed over the summer found she had breached the ministerial code, the BBC said.
Ms Patel has been a minister in four Whitehall departments: the Treasury, Home Office, the Department of Work and Pensions and the now-defunct Department for International Development.
The Cabinet Office launched an inquiry into allegations about her conduct after the Home Office’s top civil servant Sir Philip Rutnam resigned in February.
Sir Philip alleged staff believed Ms Patel “created fear” in the department, a claim she denies.
The report, carried out by the Government’s independent adviser on standards, Sir Alex Allan, has not been published.
A Government spokeswoman said: “The process is ongoing and the Prime Minister will make any decision on the matter public once the process has concluded.”
But ITV reported Mr Johnson will not sack or “reprimand” Ms Patel because the PM believes her alleged misconduct was “unintentional”.
No10 has faced repeated questions over when it will be made public.
But the BBC quoted a source saying it concluded that the “Home Secretary had not met the requirements of the ministerial code to treat civil servants with consideration and respect”.
They said the probe had uncovered evidence of bullying – even if it had not been deliberate.
Another source claimed the report was “unambiguous in stating that Priti Patel broke the ministerial code and that the Prime Minister buried it”.
A minister found guilty of breaking code is usually expected to resign.
But Mr Johnson will only issue the Cabinet Minister with a written warning rather than sack her, according to the Financial Times.
It said the PM intends to “fudge” the outcome of the inquiry, which has “robust criticisms” of Ms Patel’s behaviour.
Shadow Home Secretary Nick Thomas-Symonds said today: “These revelations could not be more serious.
“This has all the hallmarks of a cover up from the Prime Minister and raises fundamental questions about his judgement.
“His actions are all but condoning bullying in the workplace.
“In any other area of life this would not be acceptable.
“Yet again, it seems to be one rule for them and another for everyone else.
“The report needs to be published in full immediately and both the Prime Minister and Home Secretary must come before Parliament to answer questions on this mess.”
Earlier this week former Cabinet Secretary Lord Mark Sedwill suggested there could be a “wider range of sanctions” than simply expecting a minister found guilty of breaking the code to quit.
He told MPs on the Public Administration and Constitutional Affairs Committee: “I don’t think it should be binary between let off or sacked.”