Ex-Cabinet Secretary Lord Sedwill has said he will "undoubtedly" try to "see if I can grab" the role of Nato secretary-general when it becomes free.
But he told the BBC's Political Thinking with Nick Robinson podcast this might be difficult, as the job is normally done by a former politician.
"One has to recognise the realities of this," Sir Mark added.
He left the civil service last summer amid reported rifts with Boris Johnson and his advisers.
Lord Sedwill's departure came after just two-and-a-half years as cabinet secretary, a role he held while also acting as national security adviser.
But he told Nick Robinson he had "always" had "good" relationships with the prime minister and his chief adviser, Dominic Cummings, who himself recently stood down.
He and Mr Cummings had "had a drink" occasionally to discuss issues affecting the government, he said.
Current Nato Secretary-General Jens Stoltenberg - a former prime minister of Norway - is set to remain in post until September 2022.
Last summer, it was reported that Mr Johnson had promised to back Lord Sedwill as his replacement, and in an interview with BBC political editor Laura Kuenssberg in October he said he was "flattered" to be thought of as a candidate.
But he appeared to go further in expressing his ambition when telling Nick Robinson: "It's immensely flattering to be considered that I might be credible.
"It's some way off but I'm tempted to say that if the ball came loose at the back of the scrum, to use the analogy, and as a huge rugby fan, I would undoubtedly see if I could grab it."
The last UK holder of the office of secretary-general was former Defence Secretary Lord Robertson, from 1999 to 2003.
The first person to carry out the role, from 1952 to 1957, was Lord Ismay, a former chief of staff to prime ministers Sir Winston Churchill and Clement Attlee.
Lord Sedwill said: "The only time it's ever been done by someone who wasn't a politician was right at the beginning of Nato's life.
"It's always been defence, foreign and prime ministers. One has to recognise the realities of this and I'm deeply flattered and committed to the organisation."
He served as Nato's senior representative in Afghanistan from 2010 to 2011, having joined the Foreign Office in 1989.
Dave Penman, general secretary of the FDA senior civil servants' union, called Sir Mark "one of the most talented public servants of his generation", with "a long career in some of the most difficult diplomatic and security roles across the globe".
He added: "Given that experience and a lifetime of public service, it can be no surprise that he would both want, and be an outstanding candidate for, the Nato secretary-general role."
Looking back on his time as cabinet secretary, Sir Mark said that, when Mr Johnson became seriously ill with Covid last April, "the sheer impact on governance came home to us".
"We discussed with the prime minister what would happen if he was incapacitated and that [Foreign Secretary and First Minister of State] Dominic Raab would step in," he said.
"The risk of him being very seriously ill and maybe even dying of the disease was far from zero and the impact was strong emotionally and politically on everyone involved. What worried everyone was that it would debilitate him for a considerable period."
But Mr Johnson was able to return to work in late April, three weeks after being taken ill.
The full Political Thinking with Nick Robinson podcast will be published on Friday and will be broadcast on BBC Radio 4 on Saturday at 17:30 GMT.