In recent years, label-free microscopy has gained momentum over the well-established fluorescence microscopy, as it allows overcoming many important drawbacks related to the staining process. Among the label-free imaging techniques, quantitative phase imaging (QPI) has emerged since biophysical properties of cells and tissues are measured. The latest development of QPI is tomographic phase microscopy (TPM), which allows reconstructing the 3D volumetric distribution of the refractive indices (RIs) at the single-cell level by combining multiple phase-contrast maps recorded all around the sample. Very recently, the TPM paradigm has been even demonstrated working in flow cytometry (FC) modality, thus opening the route to the label-free, 3D, quantitative and high-throughput recording of living suspended cells. Nevertheless, the several advantages of QPI and TPM over fluorescence microscopy are counterbalanced by the lack of intracellular specificity due to the stain-free imaging modality. In fact, the inner cell contrast usually is not enough to properly recognize the several organelles, thus preventing intracellular studies. In QPI and in static TPM, virtual staining has been proposed as a solution, based on the training of deep learning strategies to numerically emulate the chemical staining process. However, the virtual staining approach cannot be replicated in the TPM-FC technique since a dataset of paired 3D RI and fluorescent tomograms of cells cannot be created. Here we show a computational method for the stain-free segmentation of the nucleus in 3D inside the TPM-FC tomograms of flowing cells based on an ad hoc clustering of the intracellular voxels according to their statistical similarities.