Gotham star David Mazouz has an idea for a crossover with the Arrowverse. His proposed Gotham/Arrowverse crossover -- which would have to take place in Bruce Wayne's world, since "nobody in Gotham can time travel yet" -- involves a "Flashpoint" rehash and a world out of whack.
"The Flash kind of had their run-in with Flashpoint a couple of seasons ago. Maybe there could be another kind of Flashpoint where Flash runs back in time and goes to Gotham and maybe tries to stop Bruce Wayne's parents' murder from happening," Mazouz posited to ComicBook.com. "Maybe not the traditional 'Bruce Wayne gets murdered instead and Thomas becomes Batman thing,' but something along those lines where the whole world gets whack and it's up to Flash to fix things in Gotham."
Here, Mazouz is referring to The Flash story where Barry Allen goes back in time to stop his mother's murder, resulting in a world where Atlantis is at war with the Amazons and Thomas Wayne became Batman. The CW's Flash adapted this storyline on a smaller scale in the beginning of Season 3; the Arrowverse's "Flashpoint" timeline was more or less erased after the Season 3 premiere, though Barry suffered the consequences for the remainder of the year.
Gotham has existed in its own universe since it premiered in 2014; unlike its Arrowverse compatriots, the show airs on Fox. However, the Arrowverse has a history of inter-network crossovers. Though Supergirl aired its first season on CBS, the series had a one-episode crossover with The Flash. Supergirl later switched networks and joined Arrow, The Flash and DC's Legends of Tomorrow on The CW, where it has become a part of increasingly complex four-show crossovers.
The Arrowverse shows also have a penchant for time travel and interdimensional shenanigans. Thanks to Flash's speed, he can travel backwards and forwards in time -- something that would be crucial for Mazouz's plan to work. What's more, the Arrowverse has played with the idea of parallel Earths, which would allow Gotham to continue to play by its own in-universe rules in much the same way Supergirl does. Nevertheless, it seems unlikely that Gotham will cross over with the Arrowverse shows at this point, despite Mazouz's enthusiasm.
Gotham stars Ben McKenzie as James Gordon, Donal Logue as Harvey Bullock, David Mazouz as Bruce Wayne, Robin Lord Taylor as Penguin, Cameron Bicondova as Selina Kyle, Erin Richards as Barbara Kean and Sean Pertwee as Alfred Pennyworth.