This paper, which is the first part of a study on multi-stage recuperative Brayton cycle configurations, evaluates the thermodynamic and economic feasibility of hybridizing different multi-stage recuperative Brayton cycle configurations with a solar power tower using a pressurized air receiver. In part 2 of this work, the waste energy recovery from non-solar multi-stage recuperative Brayton cycle configurations is evaluated from both thermodynamic and economic viewpoints. The results of this first part of work show that the employment of multi-stage recuperative Brayton cycle configurations leads to a significant increase in the thermal efficiency and a reduction in the fuel consumption, CO2 emissions and levelized cost of electricity (LCOE) for both non-solar and hybrid solar power plants. For non-solar power plants, the cycle configuration with 4 stages of intercooling and reheating showed the highest thermal efficiency (53.6%) and the lowest LCOE ($57.80/MWh) leading to a 32% increase and a 17% decrease compared to a simple recuperative Brayton cycle. Results of this study demonstrate that hybridization of multi-stage recuperative Brayton cycle configurations with a power tower plant with a pressurized air receiver is not economically and environmentally attractive at current time. The main reasons are the technological limitations of pressurized air receiver due to lower temperature (1223 K) and pressure (30 bar) as well as the high cost of solar power tower system (especially the heliostats). Advances in the future that enables a higher output temperature and pressure for the receiver as well as reduction in the heliostats and receiver costs would certainly be useful in improving the economic and environmental attractiveness of such hybridizations.