We're getting another Suicide Squad movie whether want one or not. Joel Kinnaman, who stared as Rick Flag in the first movie, was being interviewed by The Hollywood Reporter about his part in the fifth season of House of Cards. The interview did bring up the sequel and Kinnaman revealed that he's pretty sure he knows when production is going to start.
As far as I know they're writing the script and I think the plan is to shoot it sometime in 2018, but that could change. I think I'll definitely come back for it.
The movie has no director yet but there have been some names floating around including Mel Gibson. David Ayer does not appear have plans to return for the sequel as he's making Gotham City Sirens. If given a choice as to who he would want directing through Kinnaman would love for Ayer to return.
Ultimately, I'd love for David Ayer to direct it, but if he doesn't want to direct it then someone who is great with character and that's able to ground the story and maybe put these characters in a more normal situation. It would be really interesting to see these crazy characters interact with regular people as well.
At the moment we know that Adam Cozad (The Legend of Tarzan) is writing the script. There is currently no word on returning cast or even a proposed release date but if production is starting next year then 2019/2020 is the best guess.