I can't see this happening without either Windows getting in the way, negating much of the advantage of a console (have a look at the Windows handhelds and how they're not selling and how they're not a great experience), or Microsoft swallowing a massive part of their pride. Valve started directing work towards Linux literally because of Microsoft trying to close down the Windows ecosystem,[1] and Valve wanted an escape route if Microsoft decided to actually do that.

MS crawling on their knees to Valve to get them to cooporate on something (and Valve saying yes!), or MS figuratively doing the same by undoing all the problems MS have made for themselves with Windows and making a decent 10-foot UI so you'd actually want to use Steam on your Xbox, both seem incredibly unlikely.

Not to mention that this is more or less just admitting defeat for MS, leaving every single penny of profit in PC and Xbox gaming to Valve, other than what's directly tied to the hardware, which isn't where any of the profit actually lies.

[1] https://www.pcgamer.com/gabe-newell-i-think-windows-8-is-a-c...