In the present study, a compact heat exchanger for cryogenically fueled gas turbine engine applications is introduced. The proposed concept can be integrated into one or various vanes that comprise the compression system and uses the existing vane surface to reject core heat to the cryogenic fuel. The requirements for the heat exchanger are defined for a large geared-turbofan engine operating on liquid hydrogen. The resulting preliminary conceptual design is integrated into a modified interconnecting duct and connected to the last stage of a publicly available low-pressure compressor geometry. The feasibility of different designs is investigated numerically, providing a first insight on the parameters that govern the design of such a component.