It’s coming right down to the wire for “Supergirl.”

CBS boss Leslie Moonves is deep in talks with Warner Bros. Television about the fate of its super-expensive comic-book series starring Melissa Benoist, which wrapped up a less-than-superlative first season last month.

The network would like the show to come back, sources close to the series say, but there’s a problem. The roughly $3 million per-episode price tag CBS pays to broadcast “Supergirl” — one of the highest license fees ever for a freshman show — isn’t quite justified by the ratings. Thirteen million total viewers tuned in to the heavily-promoted premiere back in October, but about half the audience bailed over the season, according to Nielsen.

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That has set the stage for a last-minute stare-down between Moonves and Warner Bros. TV chief Peter Roth. CBS will announce its fall schedule in two weeks at the upfront presentations in New York, so the clock is ticking to hammer out a deal.

Both sides have a potential out. Moonves could push “Supergirl” to The CW, which as it happens is a joint venture between CBS and Warners (Moonves and his team are responsible for programming the network). Such a switch would make perfect sense. The youth-skewing CW already has “The Flash” and other superhero franchises (there was a crossover between “Supergirl” and “The Flash” this season), and its audience is much more aligned with “Supergirl” than is CBS’ much-grayer viewership.

Fans have suggested such a move for months and lately the Hollywood rumor mill has gone into overdrive that “Supergirl” is flying to CW. But that move would be fraught for both producers and fans, as budget-conscious CW shows don’t tend to collect huge license fees for the studios. The upshot of a CW shift is that there would very likely be big budget cuts in the offing for “Supergirl.”

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No one wants to hear about cutbacks, which may explain why those close to “Supergirl” are batting down the CW speculation.

“That’s been a rumor for two years,” one talent rep insisted. “Zero fact.”

But far stranger things have happened as network bosses race to the mid-May finish line with their fall lineups.

Stay tuned, “Supergirl” fans.