Fiber Bragg gratings in single-mode fibers, used as narrowband filters, have reached a high maturity level, especially for applications in telecommunications and sensing. In spectroscopic applications, e.g. in Raman spectroscopy, fiber Bragg grating filters can be used to separate laser probing light from generated sensor light which simplifies Raman probes. For this purpose light from a sample has to be collected with high efficiency into a fiber. The light collection efficiency in single mode fibers is, however, strongly limited due to the small fiber core area. Therefore, we have investigated the possibility to use single-mode multi-core fibers to increase the light collection efficiency while maintaining Bragg filter performance. An optical density filtering effect of 1.5 has been achieved with a fiber Bragg grating in a 61-core fiber. Simulations have been performed in order to clarify the influence of the fiber geometry and refractive index distribution on grating performance. The application of chirped gratings in the multi-core fibers improves filter performance in comparison to homogeneous gratings.