The next James Bond movie is currently in production and Daniel Craig is on board to play the role one more time, but once the film is over, the world will need a new James Bond. Dozens of names have been thrown around, dating back to before Craig confirmed his return. Everybody has an opinion, and that includes former Bond girl Halle Berry.
I’d want to see Hugh Jackman or Idris Elba. I would go for him.
Halle Berry would probably have a lot of support when it came to either of these two names. Idris Elba's name has been rumored as a Bond possibility for quite some time, there were even rumors at various points that he was in talks to take the part, but Elba continuously denied those reports.
As far as Hugh Jackman goes, we know the actor had a shot at auditioning for the role back when it was last available, but turned down auditioning because he was already working on the X-Men franchise and didn't want to get buried in two major film series at once. It's unclear if he would be at all interested now that he's done playing Logan.
If there's one major stumbling block to either of Halle Berry's choices here, it's probably age. Daniel Craig is currently 51 years old. Hugh Jackman is only a year younger than that and Elba is only slightly behind at 46. When Craig was cast he was in his late 30s and one assumes that the plan would be to cast an actor at that age, if not younger, so that they can make several more movies over the next decade or so.
Still, there's no reason James Bond couldn't be an older character. In the same way that some have campaigned to see James Bond change race or gender because, in addition to the benefit of opening up the character to a more diverse cast, it would also open up the stories that could be told, allowing James Bond to age could potentially do the same thing.
Halle Berry is potentially also one of the people interested in seeing James Bond change genders. When she's initially asked who she'd like to see take over the James Bond role, she says "a woman." While she laughs it off at first and claims she was joking, many who have suggested the same thing haven't been joking.
We almost certainly won't hear anything about the future of James Bond until after Bond 25 is released. The studio won't want to suck all the air out of the new film, so even if a replacement is already being considered, and there's no way to know if that's the case, it will likely be at least a year, and probably much longer, before we know who the next James Bond will be.