This paper aims to evaluate the potential of incorporating a novel heat recovery method within the simple cycle gas turbine exhaust stacks. The proposed heat recovery system consists of the existing semi-circular sections (nose) of the silencer baffles. In this heat transfer model, gas turbine exhaust air represents the hot side which flows across the parallel silencer baffles. The cold side stream flows inside the semi-circular sections. The proposed heat extraction system offers an advantage of utilizing waste heat from the exhaust stream, without instigating additional pressure drop on the flow. In this work, heat transfer analysis was carried out to estimate the availability of sufficient surface areas in the aforementioned sections of the silencer. The proposed model was implemented for the application of fuel gas heating such to enhance the gas turbine cycle performance. The obtained results showed that by using the nose section area of the silencer baffles only, it was possible to recover about 2.7 MW from the total energy available in the exhaust which is normally released in the simple cycle gas turbine exhaust stack. The extracted heat met almost 54% of the heat required to heat the fuel gas in the performance heater. The paper also presented further enhancements that can be incorporated, such as utilizing the downstream end of the silencer baffles. In addition, the proposed system can reduce fuel consumption, while avoiding undesired pressure drop in the exhaust system.