It would be the fifth highest chase in Test history.
Australia will need to make the fifth highest chase in Test history to win the Ashes series after England set them a target of 399 on the fourth morning at The Oval.
England lost their last two wickets for 16 runs to finish 329 all out in their second innings, setting up the final act of the campaign.
Jofra Archer was ninth man down in the second over of the morning, with Australia captain Tim Paine finally making his first successful DRS call at the last attempt.
A Pat Cummins delivery brushed Archer's glove on the way through to Paine and he finally broke his sequence of unsuccessful decisions.
Last man Stuart Broad came out swinging, launching Cummins for two steepling sixes into the leg-side but Jack Leach departed for nine attempting to get in on the act.
He aimed a big slog-sweep at Nathan Lyon and top-edged straight to Josh Hazlewood running in from mid-on.