The inquiry, which opened nine months ago, is said to be critical of Ms Patel's behaviour towards staff and will reportedly call for her to make a formal apology.
Yet the document is also said to have confirmed any bullying may not have been “intentional”, the BBC reports.
Earlier, the Financial Times said that Boris Johnson had decided only to issue Ms Patel with a written warning rather than dismissing her from the Cabinet as would normally be the case for a breach of the code.
But Labour has pushed for the long-awaited report to be published without delay claiming the findings had “all the hallmarks of a cover-up".
Shadow home secretary Nick Thomas-Symonds said: “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.”
Mr Thomas-Symonds said he had written to the chairman of the Committee on Standards in Public Life – former MI5 director general Lord Evans of Weardale – asking him to investigate Ms Patel’s conduct.
Dave Penman, general secretary of senior civil servants’ union the FDA, said: “In his foreword to the ministerial code, Boris Johnson said: ‘There must be no bullying and no harassment’.
“If, as is being suggested, substance has been found in some of the allegations against the Home Secretary, then the Prime Minister should have no choice but to conclude that the code has been breached.
“As Prime Minister, he is the sole arbiter of the ministerial code but he is also Minister for the Civil Service.
“Having pledged his support for the Home Secretary when the investigation began, and now sat on the report since the summer, he has already undermined confidence in this being a fair and impartial process.”
It has been reported that Ms Patel was subject to inappropriate treatment herself by other members of staff.
The inquiry into Ms Patel was triggered by the departure of senior Home Office civil servant Sir Philip Rutnam in March this year when he accused the home secretary of creating a climate “of fear” among her officials and a “vicious and orchestrated briefing campaign” against him.
Ms Patel has expressed concern at the “false” claims, and allies have described her as a “demanding” boss but not a bully.
Earlier this week, the former cabinet secretary Lord Sedwill told MPs the investigation was now “with” the Prime Minister, who had discussed it with his independent adviser on ministers’ interests, Sir Alex Allan.
A Government spokesman said: “The process is ongoing and the Prime Minister will make any decision on the matter public once the process has concluded.”