In Kotaku's report, they say that a source close to the deal has stated that it is "90% finished..."
Similarly, an Obsidian spokesperson said, "Unfortunately, we don't comment on rumors or speculation other than to say that the Rumors album by Fleetwood Mac still holds up".
In case you're wondering, this would be a major acquisition by Microsoft and possibly the company's biggest acquisition since they announced they had acquired Ninja Theory.
That statement seems to suggest this deal will not alter Obsidian's agreement with Private Label, but it may impact which systems the untitled Obsidian project is released for.
One source supposedly commented that Microsoft wants to increase development of PC software, making Obsidian a prime candidate for acquisition.
Microsoft has kept Minecraft multiplatform, even enabling cross-play between Switch and Xbox One players, but console makers usually buy studios with the intent for those studios to make games for their consoles, not the competition.
A person familiar with goings-on at Microsoft said the company has been looking to bolster its PC development, which makes the PC-focused Obsidian a flawless fit.