Closed Joule–Brayton thermodynamic cycles working with carbon dioxide in supercritical conditions (sCO2) are presently receiving great attention, for their multiple attractive aspects: high energy conversion efficiency, compact size, flexibility of operation, and integration with energy storage systems. These features make the sCO2 technology interesting for several energy and industrial sectors, including renewable sources and waste heat recovery. A further promising area of application of sCO2 systems is bottoming gas turbines in combined cycles installed in off-shore platforms, where the lack of space complicates the application of steam Rankine cycles. The use of steam implies large-scale components and demands for large space availability for the plant installation; in such context, the combination of gas turbines with sCO2 cycles could open the way for developing novel combined cycles, which could be attractive for all the sectors which might take advantage from the footprint savings, the enhanced flexibility, and the fast dynamics of sCO2 systems. In this work, we investigate the thermodynamic potential of combining sCO2 cycles with an existing gas turbine for off-shore applications. We consider a midsize (25 MW) gas turbine available on the market and perform a series of thermodynamic optimizations of the sCO2 bottoming cycle to maximize the exploitation of the heat discharged by the gas turbine. We analyze four alternative configurations and include realistic technical constraints, evaluated by leveraging on the most recent technical outcomes from ongoing sCO2 research projects. A comparison is also proposed with a state-of-the-art steam Rankine cycle, in terms of system efficiency and footprint of the largest components. This study clarifies the advantages and challenges of applying sCO2 in combination with gas turbines, and it confirms the relevance of sCO2 systems for off-shore applications, calling for further technical studies in the field.