This paper presents numerical investigations into the effect of feedback phase on the stability of semiconductor nanolasers (SNLs) in presence of the external optical feedback (EOF). For this purpose, numerical solutions are obtained from rate equations where the effects of Purcell cavity-enhanced spontaneous emission factor F and an enhanced spontaneous emission coupling factor β are included. In this way, a phase-insensitive stable SNL is identified when the feedback coupling fraction is below a critical threshold, ηc. Furthermore, the relationship between ηc and two other important system parameters, namely the injection current (Idc) and the initial external cavity length (L0), is studied. The results show that ηc has a bi-exponential relationship with either Idc or L0. Moreover, the influence of F on the ηc is evaluated and it is found that ηc increases with the increase of F. The results presented in this paper provide practical guidelines for the design of phase-insensitive stable SNLs which are useful for densely integrated photonic circuits based applications such as optical communications and sensing.