The ONE FC heavyweight world title is currently vacant and the British fighter believes it should be decided by a fight between himself and the Filipino-American fighter.
Parry was quoted by Rappler saying that Vera, who fought some of the biggest names in MMA when he was with the UFC, should fight him for the belt.
He said: "I'm undefeated and I'm a title contender; so therefore, that makes me the guy to fight for the title. Do you not want to best yourself by fighting the best guy? I do. That's why I'm choosing you [Vera]. I have asked enough. I called him out on social media. In fact, the fans voted for me versus Vera as one of the top fights to be seen in 2015. The best way is to stay on it.
"I don't think he's scared. I think he sees me as a difficult guy to fight.
"In terms of experience, he surely does feel that he can walk through me with all of the guys he fought. Well, I'm an easy fight for you, so you got nothing to lose but all to gain. If you're still in the game for glory and not just the money, then accept the fight. It's that simple."
Parry concluded: "If he beats me for the title, not only he becomes a champion, he becomes the first guy to give me a loss. I don't see as a bad thing."