I don't see it happening. The trend is to move towards x86, and so, I'd predict the next Intel atom.

ARM CPU's are already way cheaper than AMD or Intel it's whether they can become superior enough to the current Jaguar cores in performance to make the lower cost worth the performance loss of not choosing Intel or AMD.

And with AMD considering breaking itself up to sell off bits rather than just shutdown it is possible ARM maybe in consoles future.

Of course the console makers could just use todays Atom chips they use less than half the power, have high clockspeeds and vastly outperform Jaguar now let alone in 2018 onwards when the next consoles start picking specs.

Buy the time the next consoles are out even budget ARM chips will be vastly better than whats in the PS4 and Xbone.  The question will be is will Intel or AMD be offering CPU's cheap enough.  An 8 core ARM CPU today is $10-$15 while Intel wants 3-4 times that.

The current console CPU is so low end that getting 4-5 times more performance for less than half the power requirement can be done today let alone in 3-4 years when the next gen consoles start looking to fix specs.

Hahahahahahahahahahahahahahahahahahahahaha!!!!!!!!!!!!

No. You are wrong. You are so wrong that I can't even start to explain why you are so wrong. For you to be as wrong as you are just tells me that there is no reason to bother trying to explain it to you. 

- Moderated, Carl

PS4 already has an ARM processor, for doing all the background and standby tasks

The 3DS as well. 

https://en.wikipedia.org/wiki/Nintendo_3DS

Handhelds have been using ARM processors for ages now. The GBA had an ARM7, DS an ARM9, 3DS ARM11 Dual Core, New 3DS ARM11 Quad-core, and Vita an ARM Cortex A9 Quad core. 

The next nintendo handheld form-factor will probably use an ARM-based processor, and if fusion happends how I expect it to, the NX should have an ARM-based processor, whether or not it will be a secondary process (for OS, handheld games, or sound) or its main processor is to be determined. 

Depends on when you and he think the next consoles will be out and the magnitude of "vastly." The Jaguar, at the very least, is pretty weak. 

http://www.notebookcheck.net/SoC-Shootout-x86-vs-ARM.99496.0.html

The Jaguar is quite high up there right now  in 2013 versus top-end mobile processors and the ones in the PS4/XBO are considerably more powerful than the one in the benchmark I posted. But it isn't unrealistic to think that by 2018 or 2019 there will be consumer based powerful ARM processors in media boxes and tablets that outperform the Jaguar by quite a bit. 

scince power consumption isnt anything important for home consoles at the moment x86 might be cheaper for same power. So i guess no.

ARM is fine for consoles when LESS VOLUME is the goal. As small consoles can only archived by using cool hardware which needs less power.

Thats why Amazon, Apple etc. uses ARM for the TV boxes.

If there aren't those constrains, x86 will beat ARM performance wise as those designs are decades more mature...

What we will see next gen that ALL big three will use AMD APUs for their consoles. But we will also see more SetTop-Boxes gaining games ability on ARM while offering last or last last gen graphics.

Thats why Nintendo is introducing its NX platform - so a game could have a single code base and run - theoretically - from mobile over their handheld, over settop-boxes to their console...

Actually power consumption is important as governements want to limit how much power things can use see the limits on power use with hairdryers and vacums in the EU now.