Rangers goalkeeper Alexander had been considered the front-runner to replace the injured Craig Gordon in Oslo but he appears to be willing to stand aside for his rival.
Cardiff keeper Marshall has bided his time as number three behind Gordon and Allan McGregor while they battled it out for the number one jersey.
But with both now unavailable - the latter due to a lifetime suspension - Alexander believes Marshall should be handed his big chance.
He said: "I must admit I think David Marshall will play and deservedly so. I know what it's like to be in the squad for years and be overlooked. David's been through a lot because of circumstances and he probably thinks he deserves to play. I can't really disagree with that. He's been in the squad a long time as the number three.
"Having been behind Allan McGregor, he now find himself in the number two position. With Craig out, he keeps going up the ladder and maybe thinks he's entitled to play. That's fair enough. I can fully understand that but that's the manager's decision. I've been drafted in as cover because Craig's missing. I'm just enjoying it and not looking too far ahead."