It seems, from reading the comments that there is some confusion with some members about MOSFET saturation (not to be confused with BJT saturation): -
MOSFET saturation is when the device is operating in its constant current area. It is not when in its "ohmic" area. The ohmic area is when the device can be said to be "turned on".
In Razavi's book, it says that this MOSFET will always turn on in
And here we have some confusion - to say the MOSFET will **turn on" in the saturation region is misleading but, I don't have the referenced book so I can't be sure whether this is a mistake by the OP or a mistake in the book. Or maybe the words are not interpreted well...
Going back to the circuit, the device will initially be in the saturation region as the gate-source voltage begins to rise but, if the gate-source rises high enough it will clearly be in the ohmic (turned-on) region.
So, maybe the author, if the quote was verbatim, meant to say that it will **initially* "activate" in saturation as the gate-source voltage rises past VGS(th).