The census of Galactic globular clusters (GCs) is still incomplete, and about ten new objects are supposed to await discovery, hidden behind the crowded and reddened regions of the Galactic bulge and disk. We investigated the nature of three new GC candidates, discovered in the frames collected by the Vista Variables in the Via Lactea (VVV) near-infrared survey. They will be called VVV CL002, VVV CL003, and VVV CL004. We studied the results of point-spread-function near-infrared photometry from VVV data for the three objects and their surrounding fields, the proper motion information available in the literature and, when possible, we derived the cluster parameters by means of calibrated indices measured on the color-magnitude diagrams. The evidence shows that VVV CL002 is a newly discovered, small, moderately metal-rich (Fe/H -0.4) Galactic GC. It is located at a Galactocentric distance of 0.7+-0.9 kpc, and it could be one of the nearest GC to the Galactic center. Its characteristics are more similar to those of low-mass, Palomar-like GCs than to more classical, old, and massive bulge GCs. VVV CL003 is the first star cluster discovered in the Galactic disk on the opposite side of the center with respect to the Sun, at a Galactocentric distance of ~5 kpc. Its high metallicity (Fe/H -0.1) and location point to an open cluster, but a GC cannot be excluded. VVV CL004, on the contrary, is most probably only a random clump of field stars, as indicated by both its low statistical significance and by the impossibility to distinguish its stars from the surrounding field population. We claim the detection of i) a new Galactic GC, deriving an estimate of its basic parameters; ii) a stellar aggregate, probably an open cluster, in the disk directly beyond the Galactic center; and iii) an overdensity of stars, most probably an asterism.