Rousey is the UFC bantamweight champion, while Cyborg is the Invicta Fighting Championship featherweight champion.
Cyborg says she is concentrating on her upcoming title defence against Charmaine Tweet, however, she does believe the fight fans have been calling for will eventually happen.
MMA Mania quoted Cyborg, "I think this fight will happen. I think all the fans want to watch it, and the UFC wants to make this fight. But, I am focused on my next fight now. Charmaine Tweet is my next opponent now."
Rousey will not accept the fight against Cyborg at 145, as the Invicta champion was previously found guilty of steroid use. She was subsequently banned, however, Rousey is unlikely to face her at any weight heavier than 135.
Cyborg added: "You know, I believe anything is possible. I don't know. I'm trying a diet now, and before too, but before I had an injury. I'll try. If it doesn't happen at 135, we can make 145. I don't know. But, I'm excited for this fight so I'm going to try my best for this fight to happen for all my fans, and for me and my family."
She also said she has no problem being tested: "Yeah, I went and did the tests, and I don't have any problem about this. I did four surprise tests, and I don't have a problem about this. It is my work. Everybody makes mistakes and I make one time. Now I know I did a mistake, but now, now I don't have any problems, any time, or anywhere."