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, who has been the Home Office's permanent secretary since April 2017.
They added that there had been no animosity or "blazing rows" between Ms Patel and Sir Philip but they were simply "not the right fit".
Business Minister Nadhim Zahawi told LBC radio that Ms Patel, MP for Witham in Essex, was "utterly professional" and "works day and night".
Asked whether the home secretary was a bully, Mr Zahawi said: "No, I don't think she is at all.
"I've worked with Priti in the past on several campaigns. I've known her literally for 25 years. She is a brilliant, collegiate team player."
A Home Office spokesperson said: "We have not received any formal complaints and we take the welfare of our staff extremely seriously."
Ministers do not have the power to sack permanent secretaries or other civil servants.
If a minister wanted to remove a permanent secretary, they would have to go to the prime minister and the cabinet secretary to resolve the issue.
When a new permanent secretary is appointed, the prime minister has a say after a choice has been made by an appointments panel.
Sir Philip began his current role at the Home Office 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.
Ms Patel served as international development secretary under former PM Theresa May, before resigning in November 2017.
Mr Johnson, a long-time ally, brought her back into government after becoming prime minister last July.
The FDA union, which represents civil servants, said Home Office staff were "working flat out" to deliver the department's "demanding policy agenda".
"Civil servants working in the department are used to rising to these challenges," said the union's general secretary, Dave Penman.
"Putting undue pressure and demands on committed public servants that are already overstretched does not make for good government."