A recent report that energetic particles measured in the solar wind may be influenced by solar gravity-mode (g-mode) oscillations motivated the search for g-mode signatures in the Ulysses solar wind plasma data. Ulysses solar wind plasma data from 1 March 1992 through the 12 April 1996 were examined in this study for signs of possible solar oscillations. The multi-taper method for spectral analysis was used to look for significant spectral peaks in the entire four-year data set, as well as in the smaller, more heliographically homogenous data set over the solar poles. Several frequencies satisfying certain significance requirements were found in the g-mode frequency range in both data sets that also agree with the previously published findings. However, these identifications are shown to be false detections, and hence the frequencies found cannot be identified as solar g modes.