In this work, we analyze characteristics of Ohmic, Schottky forward and reverse contact through a low-frequency noise (LFN) measurement, combining two types of metals (Pd and Au) as the source and drain (S/D) contacts that enable p-type properties in multi-layer WSe₂ field effect transistors (FETs). The LFN is one of the significant factors liming the performance of nano-scale devices such as TMDCs FETs having large surface-to-volume ratio. In addition, the LFN analysis, which relates to the device reliability, can help identify sensitive areas for current transport and evaluate the analog circuit applicability. Theoretically, the multi-layer WSe₂ has reasonable electron affinity and bandgap that can make p-channel FET using the metal with a relatively high work-function. However, it is experimentally confirmed that Schottky contact characteristics are exhibited in the multi-layer WSe₂ FETs with various metals except Pd due to the metal Fermi level pinning phenomenon. Mobility (μeff, ~87.5 cm²/V·s), one of the electrical performance extracted from fabricated devices with Pd as S/D electrodes shows a great difference from that (~0.572 cm²/V·s) of devices with Au as S/D electrodes. The measured electrical characteristics show that a Schottky contact is formed at an interface between Au and WSe₂ causing the higher LFN of the FETs than that of device with Pd as S/D electrodes. This characteristic is also verified by confirming the reduction of LFN due to the decreased effect of the Schottky property as the drain bias is increased.