From our books
When a pilot reports established on the final approach path of a pilot interpreted approach:
a) advise the pilot of the aircraft's distance to touchdown; and
b) instruct the pilot to transfer to the tower frequency.
If flying under their own nav to the aid; i.e. following a STAR or in a proc environment, it would change a bit; outside a surveillance area giving touch-miles is a bit tough.
continue approach, call the tower, clear to land, all valid responses IMHO, in different circumstances.