An enhancement of the c-axis differential conductance around the zero-bias voltage near the superconducting transition temperature $T_{c}$ has been observed in $Au/Bi_2$$Sr_2$$CaCu_2$$O_{8+x}$ junctions. We attribute such an enhancement to the Andreev reflection (AR) between the surface Cu-O bilayer with suppressed superconductivity and the next superconducting Cu-O bilayer. The continuous evolution of the differential conductance, from gap like depression to an AR-like peak structure, around the zero-bias voltage points to weakening of the barrier strength of the nonsuperconducting layer between adjacent Cu-O bilayers as temperature approaches $T_{c}$ from below. The peak structure disappeared just below the bulk $T_{c}$ value of underdoped Bi2212 single crystals, whereas it survived up to ~1 K above $T_{c}$ in Junctions prepared on slightly overdosed crystals. According to a recently proposed theoretical consideration, a wider temperature range of the AR a bone $T_{c}$ is expected in the underdoped regime when phase-incoherent preformed pairs emerge in the pseudogap state. Our result is in contradiction to the preformed pair scenario. scenario.o.