We present a comparative multiwavelength analysis of water-maser-emitting regions and non-maser-emitting luminous 24{mu}m star-forming regions in the Andromeda Galaxy (M31) to identify the sites most likely to produce luminous water masers useful for astrometry and proper motion studies. Included in the analysis are Spitzer 24{mu}m photometry, Herschel 70 and 160{mu}m photometry, H{alpha} emission, dust temperature, and star-formation rate. We find significant differences between the maser-emitting and non-maser-emitting regions: water-maser-emitting regions tend to be more infrared-luminous and show higher star-formation rates. The five water masers in M31 are consistent with being analogs of water masers in Galactic star-forming regions and represent the high-luminosity tail of a larger (and as yet undetected) population. Most regions likely to produce water masers bright enough for proper motion measurements using current facilities have already been surveyed, but we suggest three ways to detect additional water masers in M31: (1) reobserve the most luminous mid- or far-infrared sources with higher sensitivity than was used in the Green Bank Telescope survey; (2) observe early-stage star-forming regions selected by millimeter continuum that have not already been selected by their 24{mu}m emission, and (3) reobserve the most luminous mid- or far-infrared sources and rely on maser variability for new detections.