Pete Docter said he wasn't interesting in having a role similar to Lasseter's at Pixar. Of course, that was in 2009. He may have changed his mind since then.
Q: Would you be happy in a John Lasseter role, where you aren’t making movies so much as supervising five different guys making five different movies?
Pete Docter: Man, I look at the job that guy has, and I would fail miserably. [Laughs.] He’s amazing. Just all the different things he has to balance, and I don’t know how he fits it all in his head. It’s absolutely amazing. I do not want his job.[Laughs.]
Source:
https://film.avclub.com/pete-docter-1798216800
Andrew Stanton seems more interested in pursuing live-action filmmaking than overseeing Pixar (I get the same vibe from Brad Bird too). Stanton has a pretty big ego though so he might accept if they offer him the position.
Andrew Stanton wrote:I wanted to get back into live action after four years of doing another animated feature, and I thought well, maybe TV would be the way in, because I was really done with a multi-year commitment to anything and even live action features can be over a year. I thought TV might be good: maybe a month or two on something.
Source:
http://www.sundayguardianlive.com/movie ... fter-pixar
Q: What’s next for you?
Andrew Stanton: I’ve got an independent feature that I’m trying to get off the ground called “Revolver.” It’s actually written by Kate Trefry, who wrote Episode 6 of “Stranger Things,” but it was a different route through which I connected with the script. Right now I’m back at Pixar. Part of my job is to be one of the creative overseers of the projects going on here. I spend half my year here, keeping that all going. Hopefully I’ll be doing more TV. I want to be all over the map.
Source:
https://www.nytimes.com/2017/10/31/arts ... anton.html
There are other internal candidates such as Lee Unkrich and Darla K. Anderson but I doubt either of them will get the job. I think Jim Morris and Ed Catmull will end up running Pixar in terms of management and the Brain Trust as a team will be overseeing its creative output.