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We report thermal conductivity measurements of porous Vycor glass when it is empty and when the pores are filled with helium between 0.06 and 0.5 K. The filling of liquid ^3 He and liquid ^4 He inside the Vycor pores brings about two to three-fold reduction of the thermal conductivity as compared with empty Vycor. This dramatic reduction of thermal conductivity, not seen with solid ^3 He and ^4 He in the pores, is the consequence of hydrodynamic sound modes in liquid helium that greatly facilitate the quantum tunneling of the two-level systems in Vycor and enhance the scattering of the thermal phonons in the silica network.