We investigate the near-tip region of a hydraulic fracture propagating in a homogeneous poroelastic medium. The fracture is modeled as a steadily moving semi-infinite plane strain crack. Fracture propagation is governed by linear elastic fracture mechanics. The fracturing and reservoir fluids are assumed to be identical Newtonian liquids, and fluid exchange with the surrounding porous medium is treated as a two-dimensional process. The formulation accounts for both direct contributions (mechanical and hydraulic) and cross-coupling contributions (hydraulic-to-mechanical and mechanical-to-hydraulic) to the normal stress and pore fluid pressure on the fracture surfaces. Their distributions are described by boundary integral equations that, together with the closure relations, the fracture propagation criterion, and the lubrication equation, constitute the governing system. After normalization, the problem is controlled by four parameters: scaled permeability, scaled effective confining stress, poroelastic stress coefficient, and normalized difference between undrained and drained Poisson's ratios. Numerical simulations are performed over parameter ranges representative of oil-saturated sandstone reservoirs. A comparison between the fully coupled and uncoupled models reveals that poroelastic coupling becomes increasingly significant with higher permeability, larger poroelastic stress coefficient, and initial reservoir conditions approaching depletion, resulting in substantial modifications to the fracture opening and fracturing fluid pressure profiles.