There’s no escape from all the DC TV crossover of late, with Flash-es and Arrow-s turning into Legends, even as Supergirl remains isolated at CBS for another seven episodes. We’ve heard what bosses have to say on bringing Kara Zor-El into Barry and Oliver’s world, and vice-versa, but despite a recent rumor, executive producers assure that Supergirl won’t be meeting The Flash just yet.

Over the weekend, a rumor emerged suggesting Supergirl would bring Barry Allen to National City for sweeps week in May, also insinuating it as a condition of Supergirl’s full season order. Granted, Supergirl’s ratings haven’t quite grown in the manner CBS had hoped, mutual executive producer and DC guru extraordinaire Greg Berlanti flatly denied the report at an Arrow-Flash crossover screening:

No, only because we just received the pick up. Not at this point.

Of course, should a crossover ever actually occur, it might make more sense for The Flash to drop by Supergirl, given the former’s exploration of parallel Earths, and the latter’s establishment of Superman as its realm’s only major hero. In any case, former CBS boss Nina Tassler previously downplayed the likelihood of crossover, saying “I think we’re going to keep Supergirl to ourself right now.”

There’s no telling just yet if Supergirl’s cooling buzz could actually influence CBS to stage a crossover (the network at least partially owns The CW), but consider this one debunked for now. Looks like The Flash will have to keep content crossing over with every other DC hero in the ‘verse.