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Marshall claimed all the world super-middleweight titles with a majority decision victory over Franchon Crews-Dezurn following a gruelling, physical fight at The AO Arena in Manchester on Saturday night.
Victory for the Hartlepool boxer prompted immediate talk of a second fight against Shields, who was watching from ringside, but America's multi-weight champion insisted that Marshall must now travel to her home country.
"If Savannah comes to the USA, I will fight her at whatever weight she wants to fight at," Shields told Sky Sports.
"She is going to get beat up in America, that's what is going to happen.
"[I saw] a lot of weaknesses and she didn't learn from her last night.
"I agreed with the first judge who had it 95-95.
"The fight was close.
"I expected a better performance from both girls."
Marshall suffered a unanimous decision loss to Shields in an undisputed world middleweight title fight at The O2 in October, but she hopes her rival will step up a division for the return bout.
"Sweet dreams," Marshall told Sky Sports. "I can't describe how I'm feeling at the minute.
"I think I broke my hand on her head, a tough, tough woman.
"Some of the rounds were close, but I felt like I landed the cleaner work.
"If she (Shields) wants it (the rematch), let's do it.
"I'm sure she'll want to try and unify another division."
Promoter Ben Shalom is confident that Shields will be tempted up to a higher weight.
He told Sky Sports: "She (Marshall) could've taken much easier options but this shows what a champion she is. This is her weight. This is where she feels comfortable.
"She's deserved this. She's put in everything and I'm delighted for her. What's next? I think we know what's next.
"I think it has to be at super-middleweight, that's where Savannah is the best fighter in the world. That's where the rematch has to happen.
"The support Savannah has, I've never seen anything like it. She's done The O2, she's now done the Manchester Arena, it's incredible and she deserves this. What a people's champion she is!"