But weight-wise, he could if he wanted to.
Wearing jeans, Penn (16-7-1) weighed-in at 167.2 pounds during Saturday's official UFC 127 weigh-in at Acer Arena. Fitch (23-3) came in at 169.8 pounds. Both were under the welterweight limit of 171 pounds.
Penn, who holds a 2-3 record as a welterweight, looked excited to be on the stage during the weigh-in, which was packed with Australian fans.
"This is huge and I want to thank Australia," Penn said. "I'll do my talking in the ring tomorrow."
A future shot at the welterweight title could be on the line when the two meet Sunday afternoon. The pay-per-view event will air live in the United States at its normal time of 10 p.m. ET.
While the majority of Penn's fights in the UFC have taken place with a belt on the line, it's a situation Fitch has known only once. He dropped a unanimous decision loss to George St. Pierre in his only title fight in August 2008.
Fitch has tried to downplay title talk heading into the fight, simply saying he considers it an honor to fight Penn.
"I'm pumped to be fighting B.J. Penn," Fitch said. "He's a legend, but I've got to beat him. He has what I want."
All but one of the 24 fighters made weight for the event. Lightweight Dennis Siver came in at 156.5 pounds for his fight against Australian George Sotiropoulos. He was given one hour to lose the half pound.
Brett Okamoto covers mixed martial arts for ESPN.com.