Recently, the CERN ALICE experiment observed muon bundles of very high multiplicities in its dedicated cosmic ray (CR) run, thereby confirming similar findings from the LEP era at CERN (in the CosmoLEP project). Originally, it was argued that they apparently stem from the primary CRs with a heavy masses. We propose an alternative possibility arguing that muonic bundles of highest multiplicity are produced by strangelets, hypothetical stable lumps of strange quark matter infiltrating our universe. We also address the possibility of additionally deducing their directionality which could be of astrophysical interest. Significant evidence for anisotropy of arrival directions of the observed high-multiplicity muonic bundles is found. Estimated directionality suggests their possible extragalactic provenance.