Maser emission of SiO, H$_2$O, and OH is widespread in asymptotic giant branch (AGB) stars with oxygen- (O-) rich envelopes. This emission quickly disappears during the post-AGB phase and is extremely rare in planetary nebulae (PNe). So far, only eight PNe have been confirmed to show OH and/or H$_2$O maser emission, and none have ever been found to show SiO maser emission. We intend to obtain the first detection of a SiO maser from a PN. Such a detection would provide us with a useful tool to probe mass loss in PNe at a scales of a few AU from the central star, much shorter than the scales traced by H$_2$ or OH masers. We compiled two different samples. The first one comprises all known PNe with confirmed OH and/or H$_2$O maser emission, as well as two candidate PNe showing OH masers. For the second sample, we compiled single-dish SiO maser detections in the literature, and compared them with catalogs of PNe and radio continuum emission (which could trace photoionized gas in PNe). We identified five targets (either PN or radio continuum sources) within the beam of the single-dish SiO maser observations. We then carried out interferometric observations of both samples with the Australia Telescope Compact Array, to confirm the spatial association between continuum and SiO maser emission. We find no SiO maser emission associated with any confirmed or candidate PN. In all targets, except IRAS 17390$-$3014, there is no spatial coincidence between SiO masers and radio continuum emission. While in IRAS 17390$-$3014 we cannot completely rule out a possible association, it is unlikely that the radio continuum emission arises from a PN. The absence of SiO maser emission in PNe showing OH or H$_2$O masers is of special interest, since thermal SiO emission has been reported in at least one of these targets, indicating that SiO molecules can be present in the gas phase. Since some maser-emitting PNe show evidence of having O-rich outer envelopes, and carbon- (C-) rich central stars and inner envelopes, we speculate that SiO abundance could be very low in the central regions where physical conditions are optimal for maser pumping, and C-bearing molecules may be dominant in the gas phase at those locations.