Marshall makes her first defence of the WBO middleweight championship on Saturday, live on Sky Sports on the Conor Benn bill.
The 29-year-old is the last person to beat Shields, in an amateur bout in 2012, and a rematch as professional, undefeated world champions is one of the best potential fights in the sport.
Shields told Sky Sports that her greatness exceeds Marshall: "I'm there. They are building Savannah up to make people think it. This fight is only considered because of how great I am.
"If I didn't have all these Olympic gold medals and accolades, nobody would care about a fight between me and Savannah.
"I bounced back from that loss [to Marshall in the amateurs] to win two Olympics then turn pro and be outstanding, that's why this fight would be huge.
"Is it going to be a back-and-forth brawl? No. I would be as dominant as I am against every other fighter. Probably more dominant because she speaks so much and I want to beat her up.
"I'm great, she's good."
After winning Olympic gold twice, Shields has become the first boxer (male or female) to win the undisputed title in two divisions during the four-belt era.
The American, unbeaten in 11, is regarded alongside Katie Taylor as the best female boxer in the world.
But the only blemish to her career came as a 17-year-old when she lost on points to Britain's Marshall.
"I would love to get a fight with Savannah," she said.
"Anthony Joshua and Tyson Fury are fighting twice and I would love for me and Savannah to be co-main event.
"We could fight for all the world titles at 160lbs.
"It's a fight I would definitely win so it would be great to do it on a worldwide stage."
Marshall became a world champion for the first time with an explosive stoppage of Hannah Rankin in her most recent fight.
Rankin had previously taken Shields the distance.
But Shields hit back: "Rankin shouldn't have even been at 160lbs [where she fought Marshall].
"Even she was surprised to have knocked out Rankin. But can she knock out Christina Hammer? Can she knock out Hanna Gabriels? Could she even beat those girls?
"Look, congrats to Savannah for that win. But she took so many shots. Rankin never hit me, I was 100 per cent dominant.
"Me being beaten is hard. Me being knocked out? Not even possible."
Marshall's promoter Eddie Hearn went back and forth with Shields on social media last summer, saying: "My honest opinion is that Marshall beats you."
Shields replied: "Eddie your opinion is yours, I can't take that away from you. Get the offer right."