The Mexican government due to the need of developing and creating cutting-edge technology for application of renewable energy has created renewable energy centers to develop research projects related to solar, wind and geothermal energy. In particular, geothermal energy has been of great interest due to high geothermal energy potential reported for the country. Regarding the projects approved by the Mexican government, the Universidad Michoacana de San Nicolas de Hidalgo, has been granted with fundings to carry out the design and implementation of a geothermal-solar hybrid plant for electricity production. This project is being developed in the community of San Nicolas Simirao (Michoacan State) where geothermal energy is available and exploited from an existing geothermal well. Initially, the well ran through induction, but fluid flow was not constant for long periods and was not sufficient to obtain a full operation of the geothermal-solar hybrid power plant. Therefore, it was necessary to explore new techniques to extract geothermal energy effectively, meeting design conditions of power plant. One solution might be a geothermal heat exchanger to extract heat from the rock and carry it to the surface. Literature reports two basic configurations of geothermal heat exchangers: one of them is the Downhole Coaxial Heat Exchanger and the other one is Borehole Heat Exchanger. Before making a decision to implement one type or another, several studies were carried out by the authors of this work to determine what type of configuration was most suitable, considering in such studies technical and economic aspects that provided information to continue or not the project. Therefore, in this paper the numerical analysis of both configurations (Downhole Coaxial Heat Exchanger and Borehole Heat Exchanger) is presented. The study was conducted to determine what type of geothermal exchanger presents the best trade-off between maximum heat extraction rate and minimum length to minimize costs. A minimum temperature of 125 degrees C was proposed to reach at the hot fluid heat exchanger outlet, allowing a normal operation of the geothermal-solar hybrid plant. Through numerical analysis was deteiniined that the Borehole Heat Exchanger configuration did not present good heat extractions rates, obtaining that for 100 m length the outlet temperature of the hot fluid was even lower to that of entering into the well. This behavior was attributed to heat loss in the return pipe. For the same configuration, but using a length of 500 m, a temperature of 117.21 degrees C was reached at the heat exchanger outlet. On the other hand, the Downhole Coaxial Heat Exchanger configuration reached a temperature of 118.35 degrees C for a length of 100 m. For a length of 200 m a temperature of 131.25 degrees C was obtained, whereby the facility can operate with the minimum necessary conditions. Finally, for a length of 500 m, a temperature of 134.67 degrees C was reached, showing that this type of configuration is the most suitable to be installed in the geothermal well. Thus the Downhole Coaxial Heat Exchanger configuration has more advantages than the Borehole Heat Exchanger configuration from a technical and economic (by pipe cost) point of view.