Green has not bowled since returning as a specialist No.3 after an extended break from a stress fracture of the back.
Webster has been a revelation in his seven Tests with both bat and ball. The 31-year-old's batting average of 34.63 and bowling average of 23.25 are worth bottling.
Both were key figures on difficult batting tracks in the 3-0 win in the West Indies, where Green started to hit his straps in his new position in the order in the final two Tests.
The duo are incumbents in the Test side, but are yet to play together when both are available to bowl.
The battle for top-six spots for the first Ashes Test in Perth is intense. Usman Khawaja will open, and Steve Smith and Travis Head will line up at No.4 and No.5. The battle will continue for the other slots, but both Green and Webster have compelling claims.
Webster told AAP that Australia would pick "the best six batters" and that he was confident that could include two allrounders.
"I think there is room for both of us. It can certainly work," he told AAP.
"At the end of the day we are both vying for an allrounder spot, and the way Cameron's career is going and how well he is hitting the ball it looks like he can bat anywhere in the top seven.
"I am hoping he starts really well and continues really well to become a long-term No.3 or No.4 for Australia.
"That opens up the door for me at No.6 if I am still in the best six batters in the country, and if I can bowl and catch that is only a bonus.
"Hopefully I can keep scoring runs and be really hard to displace from that No.6 spot.
"At the moment I am looking forward to the start of the Shield season, try and get some runs (for Tasmania) and hopefully line up in that first Test in Perth."
Green said his recent progress back to bowling had been diligent, with the aim of being right to bowl in the Ashes. He has had slight technical changes, but not a complete reinvention of his action.
"It will be a slow build-up to the Ashes through Shield cricket for WA, whether that be five overs first game or 10 overs the second game," he told AAP.
"A slow build-up is the way to go about it so it pays dividends later, but I am 100 per cent right now."
When Green is back bowling it will add an extra dimension to both his own focus and the team dynamic.
Marnus Labuschagne will also be fighting hard for a No.3 recall.
"The exciting part is that there are a lot of guys fighting for a spot, which is always great for healthy competition," Green said.
"Beau has had an amazing start to his short career with three or four match-winning knocks for us already.
"I definitely feel like we both can be in the team. We are batters first and bowlers second, and both of us are happy if one is taking overs off the other. We are fine in that sense. We have got a great relationship as well. He is an absolute ripper."
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