We investigate the dynamic behavior of a two-dimensional droplet adhering to a wall in Poiseuille flow at low Reynolds numbers, in a system where one of the phases is viscoelastic represented by a Giesekus model. The Cahn-Hilliard Phase-Field method is used to capture the interface between the two phases. The presence of polymeric molecules alters the viscoelastic drop's deformation over time, categorizing it into two stages before contact line depinning. In the first stage, the viscoelastic droplet deforms faster, while in the second stage, the Newtonian counterpart accelerates and its deformation outpaces the viscoelastic droplet. The deformation of viscoelastic drop is retarded significantly in the second stage with increasing Deborah number De. The viscous bending of viscoelastic drop is enhanced on the receding side for small De, but it is weakened by further increase in De. On the advancing side, the viscous bending is decreased monotonically for Ca<0.25 with a non-monotonic behavior for Ca=0.25. The non-monotonic behavior on the receding side is attributed to the emergence of outward pulling stresses in the vicinity of the receding contact line and the inception of strain-hardening at higher De, while the reduction in the viscous bending at the advancing side is the result of just strain-hardening. Finally, when the medium is viscoelastic, the viscoelasticity suppresses the droplet deformation on both receding and advancing sides, and this effect becomes more pronounced with increasing De. Increasing the Giesekus mobility parameter enhances the weakening effect of viscous bending on the advancing side.