MOSFET regions of operation
Yes. See picture above. Let's say that Vgs is Vt + 3V, and Vds is 5V. The MOSFET is in saturation. If Vgs stays constant and Vds decreases, it corresponds to a movement following the curve and moving toward the left. If Vgs stays at Vt + 3V while Vds decreases to 2V, the MOSFET is now in the ohmic region of operation. 

Image source:
https://allthingsvlsi.wordpress.com/2013/04/04/nmos-and-pmos-operating-regions/