Openly Gay Footballer Robbie Rogers Dating Hollywood Producer Greg Berlanti

TMZ Sports has learned ... Robbie is dating Greg Berlanti -- the guy who created "Arrow," "Everwood" and "No Ordinary Family." He also wrote and produced the Ryan Reynolds disaster "The Green Lantern," but hey, no one's perfect.

Sources tell us Robbie and Greg began dating sometime around May ... roughly 3 months after Robbie went public with his sexuality for the first time.

Rogers, 26, came out in February and announced his retirement from football at the same time. But in May he reprised his career in the U.S., and he featured regularly for the Galaxy in the 2013 season.(bleacher report)