The UFC had hoped to book the fight as the main event for its Jan. 19 card in Brooklyn, New York, but sources said the fight was recently canceled after Costa suffered a minor injury.
Sources say Costa is hoping to return to action in March against Romero. However, Romero would like to stay on the Brooklyn card and fight Anderson Silva.
The UFC has yet to make a decision on what they'll do with either fighter at this time, according to sources.
This marks the second time Romero vs. Costa has been canceled. The UFC wanted to book the fight on Nov. 3 at Madison Square Garden, though Romero wasn't cleared to return so soon after having surgery to repair a broken orbital bone in the summer.