The nation's intellectual property regulator turned down an initial bid by local body Linux Australia to register the name on behalf of Linux creator Linus Torvalds in September 2005, saying the name was not distinctive enough to be trademarked.
But the US-based Linux Mark Institute (LMI), which acts for Torvalds worldwide said this week it was still considering a last-minute appeal.
"The deadline to file a response to the Examiner's rejection has not yet passed, and LMI and its attorneys are still determining if they will respond," a spokesperson for the body told ZDNet Australia in an emailed statement.
The deadline is understood to fall in the first two weeks of April.
If LMI succeeds in the appeal, it could prevent companies in Australia claiming the name as their own, or using it in trade without paying royalties to LMI. Sydney-based lawyers Truman Hoyle are acting for LMI during the appeal process.