McCullum’s predecessor, Chris Silverwood, did not survive a 4-0 defeat four years ago.
The New Zealander has a contract with England until the end of 2027 — a period that includes the next home Ashes, earlier in the same year.
But the 44-year-old said, in comments carried by British media, that his fate would be decided by others.
“I’ll just keep trying to do the job, try to learn the lessons that we haven’t quite got right here and try to make some adjustments,” said McCullum. “Those questions are for someone else, not for me.
“Sometimes you don’t win, and then those decisions are up to other people. It’s a pretty good gig, it’s good fun. You travel the world with the lads and try to play some exciting cricket and try to achieve some things.”
McCullum said he believed England had improved since he took over in 2022, when he and captain Ben Stokes came together and urged players to play a fearless form of cricket dubbed “Bazball”.
“We’re not the finished article, but I think we’ve definitely improved as a cricket team,” he said. “We’ve had an identity about us.
“You’re always looking at what you’ve got right and what you’ve got wrong, and you’re not too ignorant to admit — or too arrogant either — that you get some things wrong. (It’s OK) as long as you don’t keep making the same mistakes.”
McCullum said England must show their identity in the final two games of the series, in Melbourne and Sydney.
“I’ll always have the back of my players, and always support them, and I’ll always make sure that I’m protective of them as well in a public forum,” he said.
“That doesn’t mean you don’t challenge privately, but in a public forum, you’re always protective.
“I wouldn’t imagine anything would change in the coming days as we look to try and salvage something from this. I have conviction in the style of cricket that I try to get the teams to play, with the players that you’ve got who are suited to it.”