I believe Sony will be looking into a ps4 portable in the next few years. How long is it likely before they could sell a ps4 portable hybrid for around $400?

How much would it currently cost if possible? Any experts in this field I want your thoughts! 

The way technology advances, I'd say a couple of years.

I'm pretty sure this will be possible using Tegra Xavier, scheduled for Q1 2018, so in few months (probably). With 512 cuda cores we're talking min GTX 750 performance, so very close to the base PS4, but without clocks, bandwidths etc it's hard to say.  I'm not sure about the cost though.

Years - I don't think many people around here quite comprehend TDP limits of handheld devices, in addition to AMD's designs being quite inferior to nVidia's in that regard.

The 2700u is a 15-25w part and it can do 1.66 Tflops of compute performance with its GPU.
its on 14nm.

If they made it run all games at half resolution when as a handheld, and when docked full res. (like a switch) where it can draw like ~25watts,
they could probably make such a device today.

Weren't you convinced handheld gaming was dead before the Switch launched?

Assuming it is made by TSMC and Nvidia, and it needs to be 6 times faster than the Switch, then:
10 nm TSMC = 2x shrink, available this year already
7 nm TSMC = 2.8x shrink, 2019-2020
5 nm TSMC = 4x shrink, maybe 2021?
3.5 nm TSMC = 8x shrink, maybe 2023-2024, coincidentally also TSMC's last planned node shrink.
Add one or two years since brand-new nodes are rarely used for consoles, but accounting for more efficient GPU architectures, I'd say between 5-8 years. Let the too optimistic be reminded, of course, that the Tegra X1 once had the hype it could maybe match current consoles, and look how it turned out.

Edit - added TSMC panel from the ISS conference as evidence for any of those not used to seeing these nodes and what they really mean. Note that the increased wafer cost means every mm2 of the chip (even though transistors / mm2 still decrease in price) will be more expensive that it is nowadays, further limiting how soon the "PS4 Switch" could launch:

I would guess that a shared library handheld would wait for a new generation. That would be the best way to have games optimized at launch with the embedded capacity to scale down for handheld mode.

think it was typical draw power.

basically these small chips are limited in how much power they can draw, which limits how fast they are.

Thermal Design Power - in layman's terms, how much heat hardware produces when running usual applications it was degined for (so it's not peak).

Not entirely the same thing, but i.e. Switch undocked consumes 8.9 W with max brightness when running BotW.

So when AMD makes something that can deliver PS4 performance in about 9-10W envelope, PS4 portable will be possbile.