According to Kirkinis and Davis [J. Fluid Mech. 746, R3 (2014)], the motion of a contact line can produce a sequence of moving eddies, commonly known as Moffatt vortices. In this work, we extend the formulation given in Kirkinis and Davis for the moving contact line between two viscous fluids and a nonzero static contact angle, and we consider the flow structure in the corner between the interface and the wall. In particular, we discuss the condition for observing Moffatt vortices and we demonstrate that an infinite series of Moffatt vortices cannot be observed considering a Navier-slip boundary condition.