The broadcaster is blaming a slump in advertising, with C4 chief executive Andy Duncan saying the plan had become "unaffordable". C4 is expected to save £10m in 2009 by abandoning the stations.
Channel 4 was part of a consortium due to open 10 digital radio stations. The 4 Digital group was awarded a 12-year licence to run a digital radio multiplex in July 2007, and partners included BSkyB, Bauer Radio and Carphone Warehouse.
Media regulator Ofcom says talks will take place to assess the future of the project.