Speaking on a recent Q&A, Obsidian's Josh Sawyer was asked if he'd like to lead another Fallout project if Xbox & Bethesda asked him to. Sawyer simply responded "sure", before saying that he'd need to have the right creative liberty to work on more Fallout - or any new project for that matter.
"With any project I think it has to do with 'what are we doing? What are the boundaries that we're working within? What am I allowed to do and not allowed to do?' I think that with any IP, especially one I've worked with before, the question is 'What do I want to do this time that I wasn't able to do last time?
If those constraints are just really constraining, then it's not very appealing because who wants to work on something where the one thing they want to explore is not possible to explore. I love the Fallout IP, I think there's still a ton of stories that can be told in there and questions that can be asked about... society."
Bethesda Game Studios, the main Fallout developer since 2008's Fallout 3, will surely work on 'Fallout 5' sometime in the future. However, with The Elder Scrolls 6 set to take up multiple years of dev time from this point, it stands to reason that any BGS Fallout title is a ways off yet.
It remains to be seen whether Xbox thinks it's viable to ask Obsidian for more Fallout, but clearly, Sawyer would be up for it - if he had the license to do whatever he wants with an Obsidian follow-up to Fallout: New Vegas.