Paul secured a split-decision victory over the 39-year-old in Cleveland last month to continue his unbeaten professional career.
After the fight, Woodley agreed to the rematch terms of getting the tattoo and shook Paul’s hand in the ring, but has not followed through on the bet.
The YouTube celebrity turned professional boxer has now set his sights on agreeing a fight against either Tommy Fury or Jorge Masvidal, the 24-year-old said.
“I’m over it,” Paul told ESPN after he was asked about the rematch. “I’m leaving Tyron in the past. He didn’t live up to the bet, he didn’t get the tattoo. So the rematch just doesn’t make sense anymore.”
“If he would have gotten the tattoo right away, got 10 million views on his Instagram video, then everyone would have been super hyped, there would have been a ton of press around it.
“And I would have been sort of forced to do it. I couldn’t really deny him then, because if he’s going to be a man of his word, then I have to be a man of my word. So he f****d up. He missed out on another big payday because of his ego.”
Paul clashed with Fury following his victory over Woodley and has also traded words with UFC contender Masvidal in recent weeks.
Love Island star Fury improved his professional record to 7-0 as he won on his US debut on the Paul-Woodley undercard and Paul said the pair’s camps are in talks over a proposed fight.
“He is the quote-unquote boxer. He comes from a legendary bloodline,” Paul said. “People keep saying, ‘Fight a real boxer, fight a real boxer.’ So that fight is definitely interesting to me.
“I don’t know if his name is big enough. We’re still looking at the pay-per-view numbers that came in from the UK.”
Masvidal has urged Dana White to let him out of his UFC contract in order to fight Paul and has vowed to beat up the 24-year-old if he gets the president’s blessing.
“If Dana lets him out of his contract, that would probably be the biggest fight out of all of these that we’re talking about,” Paul added.
“I would love nothing more. It’s a good test for my skill, right? He’s the ‘Gamebred’ street fighter, with his hands. I would love that. I would love that fight.”