Overton said after the third Test, which England lost by an inning and 41 runs to concede the series: "We're going to assess it over the next couple of days," Sport24 quoted Overton as saying after the third Test.
"Melbourne might be a push but it's still an option to play at the minute," he said.
The 23-year-old made an unbeaten 41 in his debut for England and has claimed six wickets in his two matches to date.
England, who are trailing by 0-3 in the Ashes series will now play the inconsequential fourth Test beginning at the Melbourne Cricket Ground (MCG) from December 26.(ANI)