The Joker and Batman are locked in a never ending battle it seems, but that doesn't mean Joker isn't open to a conflict with other DC heroes, including the Man of Steel.
During the Suicide Squad press tour, Joker actor Jared Leto was asked about Superman, and what a showdown between the two would be like, though he would have to remember his name first (via IGN).
“Ah, 'Who?' That would probably be his answer. 'Super-who? Superboy? He sounds cute. Tights? A cape?' "
“Superman seems like a lot of fun though for the Joker. The Joker and Superman would be interesting to see onscreen because Superman’s so stoic and morally centred. I think that the Joker would really enjoy that. Superman is just the classic hero and the Joker opposite any hero would be really interesting.”
The two have had a few showdowns over the course of comics history, but one of the most notable ones was the video game based Injustice Gods Among Us, where Joker is responsible for not only killing his wife Lois Lane but also his unborn child. It isn't a far reach to figure out what happens next.
Suicide Squad had a stellar opening weekend, but fans were surprised to see just how little of Jared Leto's The Joker it actually contained, something that the intense marketing campaign didn't give any indication of. Leto is actually a bit disappointed that more of his scenes didn't make the final film, but that will more than likely make an uncut Rated R version of the film inevitable, just like Batman v Superman: Dawn of Justice before it.