Home Secretary Priti Patel has tried to move the most senior civil servant in her department, it is understood.
Responding to a report in the Times, a well-placed source told the BBC there had been a “genuine disagreement” between Ms Patel and Sir Philip Rutnam.
But they denied claims that she “bullied and belittled” officials.
The Home Office said “no formal complaints” had been made about Ms Patel, who has been home secretary since Boris Johnson became PM.
A source told BBC home affairs correspondent Danny Shaw that Downing Street had been asked to intervene to move Sir Philip, the Home Office’s permanent secretary.
They added that there had been no animosity or “blazing rows” between Ms Patel and Sir Philip but said they were simply “not the right fit”.
Sir Philip began his current role at the Home Office in April 2017, after having served as permanent secretary at the Department for Transport for five years.
The former Treasury official has also served in the Business department and at media regulator Ofcom.