We have searched for molecular gas towards the nucleus of four galaxies known to harbor a water vapor megamaser . CO ( 1 \rightarrow 0 ) emission of NGC 2639 and NGC 5506 was strong enough to allow us to map their inner regions . Weak emission from Mrk 1210 was detected and Mrk 1 was not detected at all . We report the tentative detection of the CO ( 2 \rightarrow 1 ) line in NGC 5506 . After this work , 12 of the 18 known galaxies harboring a water vapor megamaser have been observed in CO . The molecular gas content in the inner regions of water megamaser galaxies ranges from 5 \times 10 ^ { 7 } to 6 \times 10 ^ { 9 } ~ { } { M } _ { \odot } . The circumnuclear molecular gas surface density also extends over nearly two orders of magnitude . The maser luminosity is correlated neither with the total amount of molecular gas found in the inner few kpc of these galaxies nor with global properties of the molecular gas such as surface density or filling factor ; it is also independent of the infrared and optical luminosities . The only significant correlation we have found involves the maser luminosity and the low frequency radio continuum flux density . We conclude that the maser activity is intrinsically related to the energy of the active galactic nucleus whereas the intensity and even the presence of a water megamaser is independent of the molecular gas global properties such as the molecular gas content and surface density in the inner galactic regions . We have also found a possible anticorrelation between the molecular gas surface density and the rate of the megamaser variations . A higher molecular gas abundance in the inner region could lead to higher maser variability because of larger nuclear flux variations due to the more variable gas infall , and/or because of more frequent interactions of the pumping agent with molecular gas condensations .