Jager has fired rounds of 65-70-71, while Woodward has carded 68-69-69.
Luke Bleumink is at 7-under-par and in outright 4th position, two strokes ahead of Bryden Macpherson and Jordan Sherratt.
Since Thursday's opening round Jager has held the lead at these championships following an impressive 7-under-par 65 opening at Mt Lawley Golf Club. The current New Zealand Amateur Champion remains confident with his game that he'll be in with a strong showing to take his first Australian Amateur Stroke title out in Perth.
"I'm striking the ball and putting well," says Jager.
"It's not often you have both happening together in an event like this. I feel my game is there and I know within myself that I can do well in front of my local crowd."
Jager has the added advantage of having played a number of professional events recently on the Australian and Nationwide Tour. These experiences are proving invaluable to the Western Australian after a return to compete in the main Australian amateur events.
"It's been a great step up for me to play events like the New Zealand Open and some Australian Tour events," says Jager, who had a top-30 finish in Queenstown.
"You can gauge your game against players that you don't normally compete against. I found this invaluable to see where my game stands with the professionals."
The Australian Amateur Championship format has effectively two titles up for the taking, with the Amateur Stroke and the Championship proper.
At the completion of Sunday's final round the leading scorer will be named the Australian Amateur Stroke Champion, a title Bryden Macpherson won last year at Royal Queensland on a first hole play-off over Jin Jeong.
The leading 32 players then qualify for elimination match play starting Monday at Lake Karrinyup to determine the Australian Amateur Champion at Wednesday's final.
"It's a long and challenging tournament," says Jager.
"If you take out the Stroke Championship, I see that as a real confidence booster to move into the match play as the number 1 seed. That's my goal and it's what I be aiming for tomorrow."