'I think we can do it', said England coach Trevor Bayliss as his side look to save the Ashes series at Old Trafford.
In all likelihood the hosts will need to bat for the whole of day five in order to earn the draw and take the series to the final Test at the Oval.
Australia meanwhile are just eight wickets from retaining the Ashes as England fell to 18-2 late on Saturday.
Steve Smith made another impressive total of 82 in Manchester as the tourists reached 186 before declaring.
England would require an unlikely 383 runs for the win, 24 more than the target set at the dramatic Headingley Test two weeks ago.
