We present the results of 0.″6-resolution observations of CO J = 3 − 2 line emission in 10 massive star-forming galaxies at z ∼ 2.2–2.5 with the Atacama Large Millimeter/submillimeter Array (ALMA). We compare the spatial extent of molecular gas with those of dust and stars, traced by the 870 and 4.4 μm continuum emissions, respectively. The average effective radius of the CO emission is 1.75 ± 0.34 kpc, which is about 60% larger than that of the 870 μm emission and is comparable with that of the 4.4 μm emission. Utilizing the best-fit parametric models, we derive the radial gradients of the specific star formation rate (sSFR), gas depletion timescale, and gas-mass fraction within the observed galaxies. We find a more intense star formation activity with a higher sSFR and a shorter depletion timescale in the inner region than in the outer region. The central starburst may be the primary process for massive galaxies to build up a core. Furthermore, the gas-mass fraction is high, independent of the galactocentric radius in the observed galaxies, suggesting that the galaxies have not begun to quench star formation. Given the shorter gas depletion timescale in the center compared to the outer region, quenching is expected to occur in the center first and then propagate outward. We may be witnessing the observed galaxies in the formation phase of a core prior to the forthcoming phase of star formation propagating outward.