We have imaged a region of 5' extent surrounding Sgr A* in the HI 21 cm-line absorption using the Very Large Array. A Gaussian decomposition of the optical depth spectra at positions within ~ 2' ( 5 pc at 8.5 kpc) of Sgr A* detects a wide line underlying the many narrow absorption lines. The wide line has a mean peak optical depth of 0.32 +/- 0.12 centered at a mean velocity of V_lsr = -4 +/- 15 km s-1. The mean full width at half maximum is 119 +/- 42 km s-1. Such a wide line is absent in the spectra at positions beyond 2' from Sgr A*. The position-velocity diagrams in optical depth reveal that the wide line originates in various components of the circumnuclear disk (radius 1.3') surrounding Sgr A*. These components contribute to the optical depth of the wide line in different velocity ranges. The position-velocity diagrams do not reveal any diffuse feature which could be attributed to a large number of HI clouds along the line of sight to Sgr A*. Consequently, the wide line has no implications either to a global population of shocked HI clouds in the Galaxy or to the energetics of the interstellar medium as was earlier thought.