Recently Quenched Ellipticals (RQEs) are special class of non-star-forming galaxies in the nearby universe that contain substantial fractions of young stars (light-weighted stellar age < 3 Gyr). RQEs are found at the centers of lower-mass dark matter halos (Mhalo = 7×1011 to 1×1013 M⊙). Given their typical masses (Mstellar = 1×1010 to 5×1010 M⊙) and environment, theoretically, these systems should be accreting fresh cold gas and supporting active star formation (SF). Since, atomic hydrogen (HI) is indirectly related to star formation rate (SFR), characterizing the HI content of RQEs (or lack thereof) provides a unique opportunity to explore galaxy quenching. For a sample of 150 RQEs selected from the SDSS, we find no HI detections for 34% and 48% of this sample in the footprints of ALFALFA and HIPASS, respectively, which are among the best HI blind surveys. Given the median redshift (z=0.05) of the RQE sample, the 3-σ HI flux detection limits of ALFALFA and HIPASS provide upper limits of MHI = 1.7×109 to 1.4×1010 M⊙, respectively. This corresponds to an upper limit of 3% to 9% in HI gas fractions for these RQEs. Based on these preliminary findings, we are computing sensitivity limits and running HI observation mocks to propose for deep interferometric observations with uGMRT and MeerKAT (the SKA precursor) for pilot samples. We hope to better constrain the masses and morphologies of any cold HI gas in the proximity of RQEs to provide new insights into galaxy quenching.