After the target is declared and modifiers have been determined.
The basic rules describe the process of making a basic attack thus:
Choose a target. Pick a target within your attack's range: a creature, an object, or a location.
Determine modifiers. The DM determines whether the target has cover and whether you have advantage or disadvantage against the target. In addition, spells, special abilities, and other effects can apply penalties or bonuses to your attack roll.
Resolve the attack. You make the attack roll.
Faerie Fire states:
Any attack roll against an affected creature or object has advantage if the attacker can see it.
Mirror Image states:
Each time a creature targets you with an attack during the spell's duration, roll a d20 to determine whether the attack instead targets one of your duplicates.
Putting it all together:
Step 1: The attacker declares the Faerie Fire'd creature as the target. At this point, the Mirror Image kicks in. The creature affected by Mirror Image has been targeted. However, Faerie Fire's granting of advantage requires an attack roll. No such roll has yet been made.
The Mirror Image affect kicks in and (potentially) redirects the attack to an image instead of the original target.
Step 2: determine bonuses and advantage/disadvantage. If the target has been redirected to an image which, though outlined by the Faerie Fire (because they mirror the appearance of the original target which has been outlined), is not affected by it.
Step 3: The attack roll is made without advantage. The attack roll is made but it is no longer targeting a creature affected by Faerie Fire.
As a result, if an attack is made against a target simultaneously affected by Faerie Fire and Mirror Image, the roll to redirect the attack preempts the attack roll and therefore prevents Faerie Fire's benefits from applying to the attack roll against the mirror image.
However, one could subscribe to the logic of this answer on the related question. The logic of that answer, which leans towards a logical narrative explanation and away from a strict legal reading, states that the images are also affected by Faerie Fire by virtue of the fact that outlining light effect is what makes a target easier to hit.
If you use this interpretation, then the question is entirely avoidable because all possible targets are legally affected by Faerie Fire, not just visually.