Primordial Quark Nuggets,remnants of the quark-hadron phase transition, may be hiding most of the baryon number in superdense chunks have been discussed for years always from the theoretical point of view. While they seemed originally fragile at intermediate cosmological temperatures, it became increasingly clear that they may survive due to a variety of effects affecting their evaporation (surface and volume) rates. A search of these objects have never been attempted to elucidate their existence. We discuss in this note how to search directly for cosmological fossil nuggets among the small asteroids approaching the Earth. ``Asteroids'' with a high visible-to-infrared flux ratio, constant lightcurves and devoid of spectral features are signals of an actual possible nugget nature. A viable search of very definite primordial quark nugget features can be conducted as a spinoff of the ongoing/forthcoming NEAs observation programmes.