At the end of Batman v Superman: Dawn of Justice, Batman pays an imprisoned Lex Luthor a visit. Among other things (ding, ding, ding), the Caped Crusader promises the villain that Arkham is waiting for him. So now, after Lex Luthor has been confirmed to appear in the upcoming Justice League film, it makes sense for the movie to feature the asylum.
However, this was just a rumor - and it still is. Nonetheless, according to Batman News, there is truth to it. Citing various sources, the website notes that multiple extras from Justice League have updated their IMDB pages, revealing the characters they will portray. The characters are simply named Arkham Guard 1 or 2 and even Lex Luthor Guard.
Of course, IMDB is not exactly the website to search for actual news (especially when it comes to big movies like this one). But when this website makes mistakes, they are usually related to the bigger names involved in projects (for example, for quite a while, Karl Urban was rumored/listed as an actor in Aquaman).
It makes sense to feature Arkham in Justice League, because this provides an opportunity to introduce Deathstroke. Some speculate that the supervillain is hired to break Lex Luthor out of the prison. It isn't said whether he'll succeed or not. However, this event will put him on a collision course with the Dark Knight, which in turn will justify the villain's presence in the upcoming The Batman movie.
If this rumor turns out to be true, it will be the second time for Arkham to be featured in the DCEU, after the fans caught a glimpse of the asylum in last year's Suicide Squad.