Bradley Cooper is allegedly an early contender for Batman in Todd Phillips’ Joker sequel, they had previously worked together on the Hangover movies. The sequel will jump forward several years and will be ignoring the age difference between Joaquin Phoenix and the child Bruce Wayne set up in the first film because who cares about continuity.
Another contender is Ryan Gosling, who currently has no projects lined up, he has been on hiatus for over a year to spend time with his family. Gosling, despite being a hot get for the Marvel and DC universes for several years (he turned down both Suicide Squad Joker and Doctor Strange, and was seen having lunch with Taika Waititi a few months ago), seems to have an open resistance to superhero films so it'll be interesting if he signs up.
The source also broke the news that The CW was forming an Arrow spinoff back in March and a Joker sequel was arriving a month before it was confirmed. But of course, it's all rumors right now.