The two companies are said to have had recent discussions over the acquisition but didn't agree on a fee.
There is no word yet on whether Microsoft will return with an increased bid.
The talks were revealed by VentureBeat's Jeff Grubb on the GamesBeat podcast, then corroborated by Eurogamer, which claimed it heard about them from a separate source.
Developer Bungie is looking for extra funding for new projects and staff, it is said. It split from its publishing deal with Activision last year and has independenly released Destiny 2 DLC since.
The studio was actually part of the Microsoft family from 2000 to 2007, but decided to leave the Halo franchise behind and go it alone. Microsoft then tasked 343 Industries with Halo sequels and remasters.
If it returns to, what is now called, Xbox Game Studios, there is no indication on what games it would work on, but would be a feather in the cap of Xbox for the upcoming next-gen console war.
We'll let you know if we hear any more on this.