The 26-year-old has never previously won a major but finds himself just one shot off the lead at Erin Hills heading into the final round.
Fleetwood triumphed at the Abu Dhabi Championship earlier this year for his second European Tour title, and Marshall expects him to do the same in the United States on Sunday.
"Knowing Tommy as I know him and seeing what he has done in the past, every time he has got within a sniff of winning a big tournament, he's gone for it 100%," he told BBC Sport.
"There's no backing down in Tommy and that's what the exciting thing is. Give him a chance on that back nine and I know he will go for it. I think he is going to do it. There is something different about him. Winners are cut from a different cloth and he is."