YouTube star Paul will continue his journey into the professional ranks of boxing when he takes on Fury, younger brother of WBC heavyweight champion Tyson, in December.
Shields is one of the most feared female fighters in the sport and will make her debut in the UK on the undercard of the Chris Eubank Jr vs Liam Williams fight next month.
The two have been trading verbal barbs for some time with Shields keen to sort out their differences in the ring.
“He isn’t even going to take an offer to come and spar me,” she told Sports Illustrated. “I have put $100,000 on the table.
“And whoever wins in sparring can walk away with the money. And I bet you will all I will walk away with the dough, Jake Paul would not risk it.
“Nobody on his team would tell him to risk it, because they know he can’t do anything with me. Despite all of my accomplishments I had this MMA split decision loss, and he was like ‘Amanda Serrano is better, she’s this and that’.
“You don’t even have an accomplishment to say my name.”
Paul’s decision to become a professional fighter followed his brother Logan’s fight with KSI in 2018, in a bout that was widely dubbed ‘the biggest event in internet history’.
Since then, the younger Paul has fought and won four professional bouts, against the likes of former NBA player Nate Robinson, ex-Bellator MMA champion Ben Askren, and former UFC welterweight champion Tyron Woodley.
“I’m the best thing that’s happened to boxing in a century, period,” Paul told Bleacher Report. “The legends would agree. The Anthony Joshuas, the Mike Tysons, the Manny Pacquiaos, the Tyson Furys. They’ve all said what I’m doing for boxing is a breath of fresh air.
“I think that debate started about a year ago – is Jake Paul good for boxing? I have silenced that, and I don’t think there’s anybody on the other side of the equation who thinks I’m bad for boxing.”