We present the first results of our X-ray monitoring campaign on a 1.7 square degree region centered on Sgr A* using the satellites XMM-Newton and Chandra. The purpose of this campaign is to monitor the behavior (below 10 keV) of X-ray sources (both persistent and transient) which are too faint to be detected by monitoring instruments aboard other satellites currently in orbit (e.g., Rossi X-ray Timing Explorer; INTEGRAL). Our first monitoring observations (using the HRC-I aboard Chandra) were obtained on June 5, 2005. Most of the sources detected could be identified with foreground sources, such as X-ray active stars. In addition we detected two persistent X-ray binaries (1E 1743.1-2843; 1A 1742-294), two faint X-ray transients (GRS 1741.9-2853; XMM J174457-2850.3), as well as a possible new transient source at a luminosity of a few times 1034 erg s-1. We report on the X-ray results on these systems and on the non-detection of the transients in follow-up radio data using the Very Large Array. We discuss how our monitoring campaign can help to improve our understanding of the different types of X-ray transients (i.e., the very faint ones).