Yes if valves pays sony and ms 300 bucks for every console sold. There is no gain for both having steam, because consoles these days are more serrvice depended than ever. Sony and MS make a lot of money from fees of games, patches, multiplayer etc.
Thats why consoles are so cheap in the first place,
just compare them with the alianware alpha how a console would be priced and have specs when just the sole system should make the console manufactors money. 150$ more than the ps4, no blu ray hardrive, mediocore dual processor and inferior ddr3 ram.

I can't imagine working out. This also probably isn't necessary in SONY's case since PS4 is getting so many of those indie pc developers anyway.

Neither Sony nor MS would see any benefit from that.That would only help Valve to enter into the console market...

Some people said streaming.But thats pointless, since you would still need a PC with hardware capable of running whatever game you want to play.Basically the consoles will just be acting as tablets or phones since it would only be receiving the video signal of the game from PC.

As of right now the XB1 could possibly run steam as a Win10 app(we still need confirmation on this.)If this were the case the games would actually be playing ON the XB1.Of course because of the limited hardware inside the XB1 ,games would probably have to be running on low graphical settings, and would compare badly to its console counterpart(if there was one.)

Yeah if Sony and Microsoft's brains broke. They have absolutely no reason to want Steam on their consoles. And Valve has already got their Steambox thing going so it's not like they have any interest in helping a competitor.

No. Steam is a rival brand. The systems have a closed OS.

Thanks for all the replies. I had no opinions really and I'm now of the idea it would benefit only valve.

Sony did not even want EA Access on their network siphoning possible revenue from them. They'd allow Steam? No way.

MS with Windows 10, who knows. Unlikely. But if they make apps/games and shit that work on all Windows 10 devices, it could be a possibility.

Half this thread is about Microsoft and it asked if it was possible on either.  

Probably because they are the one of the two where it might even be a remote possibility.

It would actually make sense to use a Wii U as the supposed steam box extension and screen mirror from your pc to your tv and/or the gamepad. A lot of pc gamers choose a Wii U as their console of choice. Very few games are on both, compared to xbox and ps who share a huge amount of games with steam, but generally steam is cheaper.