Assuming you don't have an FMS or don't want to use it for a PBD, think of the ILS as a VOR radial. You are currently at a distance x on radial a, you want to be at distance 10nm on radial b (final approach course).
Stick the Nav Display on VOR Rose mode. The larger distance (assume it's your present position) is the outer ring. For example, you are at 20 miles.
You want to go to 10nm point, so that will be halfway inside the ring. 5nm would be 75% of the way to the centre of the Rose ring, and so on. Situated on on your Final Approach Course.
Using your finger or something semi-straight (
) draw a line between your position at the outside edge of the Rose and the position of your 10nm point on the ILS.
Shift that straight edge to the centre of the Rose and read off your approximate track.
Turn on to that heading and adjust a little bit for the 20 secs of calculation time and wind.
If you really want to be deadly accurate then you can do a recalculation just before halfway (when the ILS DME reads 15nm in this case). If the new value is different, double the track error and adjust.
Edit to say: I agree with the other posters - stick it on an approximate heading and focus on the overall situational awareness and energy management instead of trying to get too accurate in this particular case. I'm also A320 btw.