One could say that the character of John Constantine has always enjoyed a certain level of cult popularity, but I think it's fair to state that he's been thrust to new heights ever since Matt Ryan took on the role in live action. After his eponymous TV series had been cancelled by NBC after only 13 episodes, Ryan continued playing the demonologist in the Arrowverse, first debuting on Arrow itself before becoming a series regular on Legends of Tomorrow. And if that weren't enough, he's even lent his pipes to a couple animated movies, those being Justice League Dark and Constantine: City of Demons.
For those unaware, John Constantine's first comic book appearance actually came via The Saga of Swamp Thing #37 in 1985, so that's why Ryan has such a desire for a live action crossover to occur. Granted, Swampy also appeared in the aforementioned Justice League Dark, but animation is a whole different ballgame.
Admittedly, I could see Constantine showing up at some point on Swamp Thing, though it's worth pointing out that competing DC TV universes tend not to overlap and cast different actors. For example, Titans recently enlisted Esai Morales as Deathstroke, whereas Manu Bennett played the mercenary on Arrow. But oddly enough, Arrow and Gotham recently featured their own unique versions of Nyssa al Ghul during the same broadcast week.
So, if Constantine does indeed make his way over to Swamp Thing at some point in the future, we'll be sure to let you know once there's confirmation. But if it happens, it's best to not act surprised if someone other than Matt Ryan is cast because of the reasons just outlined.