Askren, who was making his UFC debut, defeated Lawler in Las Vegas by first-round submission. Some -- including UFC president Dana White -- felt the stoppage was early.
After the win, White told media members he wanted to see that matchup happen again.
"We've got to do the rematch on that one," White said. "It's only fair."
Askren, appearing Monday on Ariel Helwani's MMA Show, does not agree.
"No. I didn't want to fight Robbie in the first place," Askren said. "I'm sorry that Dana's guy didn't win and he keeps pouting about it and wants to run it back, but we're just not going to do that. How does that benefit me? If I beat him again I'm not really in any better spot than I am right now."
The Wisconsin native told Helwani the UFC booked him a flight to London to see Darren Till versus Jorge Masvidal in person on March 16. Askren (19-0-1) has stated he wants to face the winner of that matchup for his next fight.
Askren is the former Bellator and ONE Championship welterweight titleholder. He came to the UFC in an unprecedented trade involving former UFC flyweight champion Demetrious Johnson in October.