Estimate has carried the Queen's colours to win the Doncaster Cup but a Melbourne Cup start appears unlikely.
Trainer Sir Michael Stoute says there are concerns the ground at Flemington might be too hard for the mare.
"I think we have to consider it, but I won't make the final decision. I'm not paying!" Stoute said.
"You'd wonder a bit about the ground at Flemington as she does like a little bit of forgiveness in it.
"We'll think about it and discuss it with the Queen and John Warren (Her Majesty's racing advisor)."
Warren's chief concern about sending Estimate across the globe to Australia would be the protection of a thoroughbred who will eventually become a most appealing prospect as a broodmare.
"Obviously the travelling is a huge ask as well, so there are many complexities," he said.
"The tempo of the race in Australia is not quite what this filly is about. This filly is about sticking it out and Australia can be a bit stop-start.
"I know there's been huge pressure from the Australians for the Queen to have a runner, understandably, which would be amazing to do and, for so many reasons, it's good.
"I sound as though I'm talking myself out of the Melbourne Cup, but there are a number of people that will have an input.
"There are only three options - Ascot (Champions Day), Paris (Prix du Cadran at Longchamp) and Melbourne. My hunch is she probably won't go to Australia.
The Doncaster Cup win came after a season with plenty of ups and downs for Estimate and the stable.
Estimate ran well when second as she tried to defend her Gold Cup at Royal Ascot but just a month a later a positive test for morphine delivered a blow which made worldwide headlines.
The mare was one of a cluster of horses to become embroiled in the case, with the source of the drug identified as a contaminated batch of horse feed.
Even so, she is still likely to be disqualified from her placing in the Gold Cup at a British Horseracing Authority hearing on September 25.
After a lacklustre performance at Goodwood, Estimate took the Group Two Doncaster Cup from Whiplash Willie by 1-1/4 lengths.