The occurrence of dripping and jetting regimes in a microfluidic coflowing injector device has been related recently to the spatio-temporal stability properties of the developed velocity profile. Dripping corresponds to an absolutely unstable flow while jetting is observed when the Rayleigh-Plateau instability of the core-annular jet is convective. In this work we take into account the effect of the entry region on the dripping to jetting transition by carrying out a global stability analysis of the steady two-phase base flow. We show that, depending on the flow parameters, the entry region can affect significantly the transition between the two regimes.