Marsh, who helped Australia negotiate 30 overs on Saturday at Old Trafford alongside Marnus Labuschagne, was nursing some soreness during the game and did not bowl on the third day.
If Marsh is unable to bowl Green's position might be safe although Australia's coach Andrew McDonald said runs were the most important factor for whoever bats No. 6. However, having that extra pace option has been vital in managing the workload of the main quicks.
"The team has played three quicks and one spinner and we have gone that way numerous times in the past," McDonald said. "We have had the luxury of allrounders, or in particular Cameron Green, that's changed the shape of the team over time. Runs were premium first and foremost."
Green's challenging Ashes
Green has struggled to find fluency with the bat on this tour, where he has averaged 19.14 against India and England and was again tentative at Old Trafford, though he got a borderline lbw decision against Chris Woakes in the first innings.
So far in his 24-match Test career, the only games Green has missed have been through injury - a broken finger suffered against South Africa last December which also ruled him out of the start of the India series, then the hamstring niggle on this tour.
Green has only had two nights at home in almost six months, having followed the India tour with a full IPL for Mumbai Indians. It was after that campaign that he squeezed in a brief trip back to Perth and joined Australia's training camp in the UK a couple of days later than others.
"He's had a different experience," McDonald said. "He's had the IPL, and people probably draw some conclusions that that's affected the way he's gone about things here. But…I think he's in a good space. I think you'll see a lot of our batters are working on the right things, and the way they go about it runs are just around the corner."
IPL adds new layer for all-format Green
"He's still young, he's still learning his trade, this is his first time in these conditions," Labuschagne said during the Old Trafford Test. "With the IPL there wasn't heaps of time to adjust but I think he's doing a good job."
Last year Green spoke about the challenge of switching between formats when he was part of Australia's T20 World Cup squad and then had a slow start to his Test season. On that occasion the lack of time in the middle was a factor with him being largely unused during the World Cup, only playing the final game against Afghanistan. He was also unable to play any Sheffield Shield cricket.
It's a situation that may confront him again this year with the ODI World Cup in October and November, though there is a possibility he won't be selected for the T20 series in India which follows that tournament and may be able to get some Shield cricket for Western Australia ahead of the Test series against Pakistan.
However, there is a good chance that Marsh now has the lead in the allrounder pecking order after his impressive return to Test cricket - a thrilling century at Headingley and two important innings at Old Trafford.
Neser could come into consideration for The Oval
"[There were] two separate incidents where he dived and landed on the point of his shoulder…then the other one he slipped down on the rope and sort of extended the shoulder joint," McDonald said of Starc. "So he's looking worse for wear and a little bit sore. All indications are that he'll be right to go but that'll be assessed.
"Everyone's on the table, every selection. And Michael [Neser] knows that. He was a serious consideration here and he was under consideration at Leeds also, so you're always sort of balancing those who are up and running in the series versus freshness."
Andrew McGlashan is a deputy editor at ESPNcricinfo