The perception of direct gaze give insights about the attention and interest of a looker. Besides the accurate perception of horizontal and vertical gaze direction, the perception of the depth of fixation is crucial to identify the looked-on object or person. Previous studies found evidence for a depth dimension of the area of direct gaze. The present study aims to identify the influence of observer-looker distance on the accepted range of convergence and divergence. The results of two experiments indicate a strong preference for parallel eyes as the perceived central depth for all distances (15 to 150 cm). Additionally, Experiment 1 provides evidence for the proximal border being closer to the looker in near distances (13° vs. 11° vergence) which reflects an overall gain in size of the proximal area for larger distances. The border minimally shifts in direction to or from the looker in dependence on the observer’s position. Overall, convergence angle corresponding to fixation distances up to of 10 to 20 cm in front of the looker are accepted by the observer relatively independent of his own position. Experiment 2 additionally, shows a rejection of the natural required vergence of 11.71° in 15 cm distance with the proximal border being less converged than necessary (10°). The distal border in both experiments was again large (10° divergence) indicating an infinite distal border. Following it is discussed if the depth dimension results in a spherical cone with its origin 10 to 20 cm in front of the looker.