Context. After the successful landing of Philae on the nucleus of 67P/Churyumov-Gerasimenko, the Rosetta mission provided the first opportunity of performing measurements with the CONSERT tomographic radar in November 2014. CONSERT data were acquired during this first science sequence. They unambiguously showed that propagation through the smaller lobe of the nucleus was achieved. Aims. While the ultimate objective of the CONSERT radar is to perform the tomography of the nucleus, this paper focuses on the local characterization of the shallow subsurface in the area of Philae's final landing site, specifically determining the possible presence of a permittivity gradient below the nucleus surface. Methods. A number of electromagnetic simulations were made with a ray-tracing code to parametrically study how the gradient of the dielectric constant in the near-subsurface affects the ability of CONSERT to receive signals. Results. At the 90 MHz frequency of CONSERT, the dielectric constant is a function of porosity, composition, and temperature. The dielectric constant values considered for the study are based on observations made by the other instruments of the Rosetta mission, which indicate a possible near-surface gradient in physical properties and on laboratory measurements made on analog samples. Conclusions. The obtained simulated data clearly show that if the dielectric constant were increasing with depth, it would have prevented the reception of signal at the CONSERT location during the first science sequence. We conclude from our simulations that the dielectric constant most probably decreases with depth.