The massive black hole Sgr A* at the very center of the Galaxy, and its immediate stellar and non-stellar environment, have been studied in the past decade with increasing intensity and wavelength coverage, revealing surprising results. This research requires the highest angular resolution available to avoid source confusion and to study the physical properties of the objects. GCIRS 7 is the dominating star of the central cluster in the NIR, so it has been used as wavefront and astrometric reference. Our studies investigate, for the first time, its properties at 2 and 10 micron using the VLTI. We aim at analyzing the suitability of GCIRS 7 as an interferometric phase-reference for the upcoming generation of dual-field facilities at optical interferometers. VLTI-AMBER and MIDI instruments were used to spatially resolve GCIRS 7 and to measure the wavelength dependence of the visibility using the low spectral resolution mode ( lambda / DELTA lambda 30) and projected baseline lengths of about 50 m, resulting in an angular resolution of about 9 mas and 45 mas for the NIR and MIR, respectively. The first K-band fringe detection of a GC star suggests that GCIRS 7 could be marginally resolved at 2 micron, which would imply that the photosphere of the supergiant is enshrouded by a molecular and dusty envelope. At 10 micron , GCIRS 7 is strongly resolved with a visibility of approximately 0.2. The MIR is dominated by moderately warm (200 K), extended dust, mostly distributed outside of a radius of about 120 AU (15 mas) around the star. A deep 9.8 micron -silicate absorption in excess of the usual extinction law with respect to the NIR extinction has been found. Our VLTI observations show that interferometric NIR phase-referencing experiments with mas resolution using GCIRS 7 as phase reference appear to be feasible, but more such studies are required to definitely characterize the close environment around this star. The MIR data confirm recent findings of a relatively enhanced, interstellar 9.8 micron -silicate absorption with respect to the NIR extinction towards another star in the central arc-seconds, suggesting an unusual dust composition in that region. We demonstrate that the resolution and sensitivity of modern large-aperture optical telescope arrays is required to resolve the innermost environment of stars at the Galactic center.