It sounds like you might only need the X,Y of the nearest instance of that object?
If that is the case then you could just use:
GML:
var target_x = instance_nearest(x, y, obj_enemy).x;
var target_y = instance_nearest(x, y, obj_enemy).y;
Called from within the player object's code.
target_x, target_y will be the coordinates of the nearest instance of "obj_enemy" to the player
or if you only want to know the id of the nearest instance of obj_enemy:
GML:
var target_enemy = instance_nearest(x, y, obj_enemy);
Then target_enemy will store the id of the nearest instance of obj_enemy
But yeah, if you do want to store all of the coordinates of each instance of obj_enemy then listen to Nocturne.
(note that I've used local variables so they wouldn't be stored for longer than the script / event runs. You can use non-local variables if you need them stored pst the end of the script)