The DCTV universe over at The CW is definitely expanding. Between Arrow, The Flash and DC's Legends of Tomorrow there are 30+ (and counting) superheroes operating in some form or fashion on The CW. It seems like a no-brainer that Supergirl would want to benefit from such a developed TV universe but CBS seems hesitant. However, a possible indication that they're warming up to the idea was the reveal at yesterday's TCA panel that the shows will have "crossover promotions".
By promotions, perhaps they mean that Supergirl could appear in the Super Hero Fight Club promotions should The CW choose to do that again for the new season? We'll have to wait and see but the majority of the fanbase for all these shows definitely want to see them crossover. Again, when Supergirl was first announced showrunner Greg Berlanti was the first to comment that the Arrow, Flash and Supergirl could crossover. CBS quickly disuaded such a notion but perhaps Berlanti is swaying minds behind the scenes?
Supergirl premieres Monday, Oct. 26 at 8:30 p.m. ET on CBS. The CW will premire Arrow on Oct. 7th at 8PM and The Flash on October 6th at 8PM.