We present the results of deep, high-resolution, multi-band optical observations of the field of the young (~ 5,000 yrs) 16 ms X-ray pulsar PSR J0537$-$6910 performed with the Advanced Camera for Surveys (ACS) aboard the Hubble Space Telescope (HST). Although a few new potential counterparts have been detected within or close to the revised Chandra X-ray error circle (~1 arcsec) of the pulsar, only two of them (with magnitudes m_{814W} ~ 23.9 and m_{814W} ~ 24.2) show indications of a peculiar spectrum which could be related to optical emission from the pulsar. This might be true also for a third, fainter, candidate detected only in one filter (with magnitude m_{814W} ~ 26.7). If either of the two brighter candidates is indeed the actual counterpart, the optical output of PSR J0537-6910 would make it similar to young Crab-like pulsars. If not, it would mean that PSR J0537-6910 is significantly underluminous with respect to all pulsars detected in the optical Comment: 7 pages, 5 figures, Astronomy & Astrophysics, in press