Microscale swimming strategies of bodies with different shapes in the presence of external flow have been studied extensively in previous literatures. However, the behaviour of the microswimmer near a wall with complex surface wettability conditions is still unexplored. To bridge this gap in literature, we consider a spherical microswimmer and illustrate its dynamic behaviour with an analytical-numerical approach near a slippery wall. The coupled effect of self-propulsion and external shear presents some new characteristics in the presence of wall slip. Intending to observe different types of possible mobility of a puller-type microswimmer, we illustrate the trajectories. Additionally, we present phase portraits to illustrate the dependence of the squirmer parameter with the background shear and slippery wall. The primary findings of the study are the combinations of external flow and slip length causing the squirmer to escape from, collide against the wall and exhibit rheotactic motion, which are summarised in the regime map. Our results reveal that a slippery wall additionally introduces a critical limit of shear strength, beyond which puller microswimmers escape for lower values of slip length followed by a band of the rheotactic and an annihilation zone against the wall at higher values of wall slip.