A fight against Marshall could be as big as the one against Serrano, says Shields.
The fight between Taylor and Serrano at Madison Square Garden in New York was described as the biggest in women's boxing history.
America's Shields is set to face long-term rival Marshall in September.
Shields believes that the storyline behind it means that it can be as big.
This fight should be happening in London because of how great I am and how she is a knockout artist.
Shields has won all 12 of her professional fights and is a multiple world champion across three weight classes.
She lost her amateur boxing career against Marshall.
Shields is the undisputed champion of the division, but the WBO title is held by Marshall.
The fighters have been critical of one another on social media, while a bout between the pair has been rearranged numerous times.
Shields doesn't respect her opponent.
She said she didn't have respect for anyone who didn't work hard.
I give credit to someone who has the belts. I'm not a three-time world champion, I'm a 12-time world champion who's fought in three different divisions since turning professional.
I beat these girls because I was great. She wouldn't have won any of that if I fought her.
The UK is building her up to be a knockout artist and they will be disappointed.
Shields signed a contract with MMA promotion the Professional Fighters League in 2021.
She has fought in the PFL twice, winning once and losing the other, with her next bout scheduled for November.
One example being that the PFL boasts a $1 million prize for winners of its annual tournaments, is that Shields turned to MMA because the sport was presenting opportunities for women that were not present within boxing.
When I signed with the PFL, boxing was going slow and I was tired of fighting for money when I knew I was worth more.
To be two-time Olympic champion, three time undisputed world champion, and also getting 90 million for it, is something that Saul is already doing.
He is a big star but I have not been given the chance to be a huge star.
Shields thinks that female boxers were denied a platform previously.
She said that people are overlooking the fact that Taylor and Serrano were the first women to perform on those platforms.
If that opportunity had been given to me in the US, we would have done great numbers, but we also need a good opponent.
People always talk about equal pay in women's boxing but they don't talk about equal opportunity and that's what women's boxing needs - equal pay.
A number of mixed martial artists have turned to boxing in recent years, but it is less common to see the move in the opposite direction.
Shields admitted that learning the ins and outs of grappling was the hardest part.
Like everyone else, I see my potential, but also my limitations. You can have all the potential in the world, but if you don't put in the work, you won't be as good as you want to be.
I haven't reached the level I want to be yet, but I'm getting there.
Shields said her drive to challenge herself was what separated her from other boxers.
She said that she believes she can do anything if she trains and works for it.
That is another reason why I am the greatest boxer of all time. Name another boxer who is doing what I am doing, who goes inside the cage with other MMA fighters and wins, and also continues to be dominant in boxing.
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