[abridged] The severe crowding in the direction of the inner Milky Way suggests that the census of stars within a few tens of parsecs in that direction may not be complete. We search for new nearby objects companions of known high proper motion (HPM) stars located towards the densest regions of the Southern Milky Way where the background contamination presented a major problem to previous works. The common proper motion (PM) method was used--we inspected the area around 167 known HPM (>=200 mas/yr) stars: 67 in the disk and 100 in the bulge. Multi-epoch images were provided by 2MASS and the VISTA Variables in Via Lactea (VVV). The VVV is a new on-going ZYJHKs plus multi-epoch Ks survey of ~562 deg^2 of Milky Ways bulge and inner Southern disk. Seven new co-moving companions were discovered around known HPM stars; six known co-moving pairs were recovered; a pair of stars that was thought to be co-moving was found to have different proper motions; published HPMs of eight stars were not confirmed; last but not least, spectral types ranging from G8V to M5V were derived from new infrared spectroscopy for seventeen stars, members of the co-moving pairs. The seven newly discovered stars constitute ~4% of the nearby HPM star list but this is not a firm limit on the HPM star incompleteness because our starting point--the HPM list assembled from the literature--is incomplete itself, missing many nearby HPM M and L type objects, and it is contaminated with non-HPM stars. We have demonstrated, that the superior sub-arcsec spatial resolution, with respect to previous surveys, allows the VVV to examine further the binary nature nature of known HPM stars. The >=5 yr span of VVV will provide sufficient baseline for finding new HPM stars from VVV data alone.
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