In the near- to mid-infrared wavelength domain, bright continuum sources in the central parsec of the Galactic center (GC) are subject to foreground absorption. These sources therefore represent ideal probes of the intervening material that is responsible for the absorption along the line of sight. Our aim is to shed light on the location and physics of the absorbing clouds. We try to find out which of the gaseous absorbing materials is intimately associated with the GC and which one is associated with clouds at a much larger distance. We used the capabilities of CRIRES spectrograph located at ESO Very Large Telescope in Chile to obtain absorption spectra of individual lines at a high spectral resolution of R=65000, that is, 5km/s. We observed the 12CO R(0), P(1), P(2), P(3), P(4), P(5), P(6), P(7) and P(9) transition lines, applied standard data reduction, and compared the results with literature data. Results. We present the results of CRIRES observations of 13 infrared sources located in the central parsec of the Galaxy. The data provide direct evidence for a complex structure of the interstellar medium along the line of sight and in the close environment of the central sources. In particular we find four cold foreground clouds at radial velocities vLS R of the order of -145, -85, -60, and -40+\/-15km/s that show absorption in the lower transition lines from R(0) to P(2) and in all the observed spectra.We also find in all sources an absorption in velocity range of 50-60km/s, possibly associated with the so-called 50km/s cloud and suggesting an extension of this cloud in front of the GC. Finally, we detect individual absorption lines that are probably associated with material much closer to the center and with the sources themselves, suggesting the presence of cold gas in the local region.