You did not say what type of tool holder you are using. You can put a piece of drill rod in place of your drill and use an indicator attached to the chuck to sweep in the drill rod and see which direction it is off.
As a work around, make your own drill holder bushing. Mount some round bar stock in your drill holder and put your drill in the chuck and drill out the bar stock. Be sure to mark the stock for alignment to the holder. Then take the bar stock out and drill and tap some set screw holes or split it on a band saw to make your own collet. Will only work for that size drill, in that holder, and probably only at that tool station.