Faucet handle base

FIG. 1 is a perspective view of a faucet handle base showing my new design;

FIG. 2 is a first end view thereof;

FIG. 3 is a second end view thereof;

FIG. 4 is a top plan view thereof;

FIG. 5 is a first side view thereof, the opposite side being a mirror image of the side shown; and,

FIG. 6 is a bottom view thereof.

The broken lines showing portions of the faucet handle form no part of the claimed design.