Full-field optical coherence microscopy (FFOCM) utilizes coherence gating to obtain high-resolution optical sections in thick tissues. FFOCM is an attractive technology for endoscopic microscopy at the cellular level since it does not require a high NA objective lens or beam scanning and is therefore particularly amenable to miniaturization. In this manuscript, we present a novel scheme for conducting FFOCM that utilizes spectrally modulated, spatially incoherent illumination and a static Linnik interferometer. This approach is advantageous for endoscopic microscopy since it allows FFOCM to be conducted through a single multimode fiber optic imaging bundle and does not require moving parts in the endoscope probe. Images acquired from biological samples in free space demonstrate that this new method provides the same detailed microscopic structure as that of conventional FFOCM. High-resolution images were also obtained through a multimode fiber bundle, further supporting the potential of this method for endoscopic microscopy.