Requirements on the double-cladding Yb-doped fiber (DCYF) for power scaling of diffraction-limited fiber amplifiers are studied in this paper. By considering the limitations of thermal lens and transverse mode instability separately, it is found that the power scaling limit can be enlarged to more-than 100 kW and 80 kW, respectively, with the proper selection of pump and signal wavelengths. It is also found that the requirements on DCYF strongly depend on the wavelength and brightness of pump light. It is predicted that smaller-than 20-µm core diameter is required to achieve the 20-kW output power, as long as the 976-nm pump brightness can be high enough. The requirements on the inner-cladding diameter and cladding-to-core ratio of DCYF are also investigated.