However, club medical staff have insisted he needs more time to recover from the ankle injury he received after clashing with Manchester City defender Vincent Kompany in the Toffees' 2-0 defeat nine days ago.
Cahill was only just passed fit enough to play in the weekend's 216th Merseyside derby but now requires a period of rest.
"Tim played through the pain barrier on Saturday against Liverpool but the scan showed that the best course of action now is rest and rehab," the club's head of medicine Danny Donachie told the club's website.
"Tim is disappointed but it is a straightforward decision because he would not be fit enough to play in the games in Australia."
The 31-year-old will now undergo intensive rehabilitation at the club's Finch Farm training ground for the next 10 days or so.