Folding and intermingling of chromosomes has the potential of bringing close to each other loci that are very distant genomically or even on different chromosomes. On the other hand, genomic rearrangements also play a major role in the reorganisation of loci proximities. Whether the same loci are involved in both mechanisms has been studied in the case of somatic rearrangements, but never from an evolutionary standpoint. In this paper, we analysed the correlation between two datasets: (i) whole-genome chromatin contact data obtained in human cells using the Hi-C protocol; and (ii) a set of breakpoint regions resulting from evolutionary rearrangements which occurred since the split of the human and mouse lineages. Surprisingly, we found that two loci distant in the human genome but adjacent in the mouse genome are significantly more often observed in close proximity in the human nucleus than expected. Importantly, we show that this result holds for loci located on the same chromosome regardless of the genomic distance separating them, and the signal is stronger in gene-rich and open-chromatin regions. These findings strongly suggest that part of the 3D organisation of chromosomes may be conserved across very large evolutionary distances. To characterise this phenomenon, we propose to use the notion of spatial synteny which generalises the notion of genomic synteny to the 3D case.