The comments come after Marsh scored a century in the third Test, replacing an injured Green in the side. It was Australia's first loss of the series away against England, but none of that was Marsh's fault.
The veteran all-rounder, long maligned by the Australian public, made as strong of a case for his retention as possible during the third Test at Headingley, with Australia still controlling the series 2-1, heading to Manchester for the fourth Test. The series will then return to London at The Oval for the fifth and final Test.
Speaking to Cricket.com.au, Marsh refuted suggestions he and Green could play in the side.
"I don't think there is [room for us both]. Unfortunately there's not, that's all right," Marsh said.
"I don't want to comment on it too much.
"Ultimately that stuff is out of my control. I've got a very, very close relationship with 'Greeny'.
"He's a fantastic young kid. He's learning on the go and we know what a super talent he is.
"It's important for him to be in our side. We've seen how important he is for our side over the last couple of years. We'll just have to wait and see."
Green had struggled before his injury, averaging under 20 with the bat and more than 45 with the ball.
Despite that, his return to fitness could see him come straight back into the side, with the highly talented 24-year-old rated strongly by Australian selectors, coaching staff and captain Pat Cummins.
Cummins himself didn't rule out the idea of both Green and Marsh playing - the only realistic way that could happen, though, is with the axing of David Warner, given all of Usman Khawaja, Steve Smith, Marnus Labuschagne, and Travis Head have their spots locked into the side.
"We'll keep all our options open. We've got nine or 10 days now, so we'll take a deep breath," Cummins said after the conclusion of the third Test.
"Greeny should be fit for Manchester, we should have a full roster. We'll have a look at the wicket, have a chat, and work out the best XI.
"It's possible (that Marsh is dropped), but it was a pretty impressive week wasn't it?"
Coach Andrew McDonald admitted Marsh had made a pretty good case.
"He's made a pretty good case, it's pretty strong," McDonald said.
"I thought he was outstanding this game, a bit of luck in that first innings (getting dropped on 12) but he took that, he was positive, showed great intent and he's a fine player of the short ball.
"There's a lot to like with how he matches up against England.
"I thought he was impressive with the ball as well, and he's done that before in England with the ball as well, so that's nothing new."
McDonald also pointed to the fact that, even with Warner's overall struggles, the Australian opening stand has gone past 50 on three occasions in six innings during the series so far, seemingly suggesting there may be no need for change.
"You've also got to reflect on what the opening partnership's been able to do across the six innings (of the Ashes series) and there's been three 50-plus partnerships in there," McDonald said.
"Albeit it didn't function to its level here, in some ways it's done well so far in this series.
"We've got a lot to consider and a lot to weigh up … we've got everything to consider in terms of Mitch Marsh coming in, what the balance looks like, our allrounders.
"We've got an extra batter who's put his hand up and we'll have to consider the options ahead."
The fourth Test gets underway on Wednesday, July 29.