In-plane dispersions of quantum well (QW) states originating from the electron confinement of Ag sp electrons within the MoS(2) band gap region are investigated by means of angle-resolved photoemission spectroscopy (ARPES). A number of QW resonances have been observed in the ARPES spectra in a binding energy range lying outside the MoS(2) energy gap which is required for full confinement of the Ag sp electrons. In spite of having the expected free electron-like behavior, these QW states show a significant increase of in-plane effective mass with increasing binding energy due to the hybridization of Ag sp electrons with the MoS(2) valence bands. The binding energy dependence of the bottom of the QW states (k(//) = 0) as a function of the Ag film thickness has been analyzed. The well-established phase accumulation model has been applied for calculating the phase shifts of electrons at the boundaries. Our observations show that the total phase shift behaves differently for energies above and below the MoS(2) valence band maxima, due to the hybridizations being different in nature. The structure plot calculated considering the different quantum number dependent total phase shifts provides a good description of the experimental observations.