Cruz, who is a former champion, was forced to give up his belt when injuries stopped him fighting for three years.
Barao (33-3 MMA, 8-2 UFC) was promoted to full champion before Dillashaw (12-2 MMA, 8-2 UFC) won the title at UFC 173.
At the FOX 16 post-fight press conference, Dillashaw said that he would like to face Cruz or Raphael Assuncao.
"I mean, it's so hard for me to think about anyone else," Dillashaw said.
"I've been thinking about Renan Barao for over a year and a half. But we've got guys like Dominick Cruz and Raphael Assuncao.
“They're both great fighters but they're hurt now. Whenever they come back, I don't know what the plan is, but I'd like to see either one of those guys. I don't know. I'm not sure."
Dillashaw said that if given the choice he would like to fight Cruz.
"That's the biggest fight," Dillashaw said. "That's what's going to make my name the biggest at this weight class, fighting Cruz as soon as he's able to come back."