The transition between massive Class II circumstellar disks and Class III debris disks, with dust residuals, has not yet been clearly understood. Disks are expected to dissipate with time, and dust clearing in the inner regions can be the consequence of several mechanisms. Planetary formation is one of them that will possibly open a gap inside the disk. According to recent models based on photometric observations, T Cha is expected to present a large gap within its disk, meaning that an inner dusty disk is supposed to have survived close to the star. We investigate this scenario with new near-infrared interferometric observations. We observed T Cha in the H and K bands using the AMBER instrument at VLTI and used the MCFOST radiative transfer code to model the SED of T Cha and the interferometric observations simultaneously and to test the scenario of an inner dusty structure. We also used a toy model of a binary to check that a companion close to the star can reproduce our observations. The scenario of a close (few mas) companion cannot satisfactorily reproduce the visibilities and SED, while a disk model with a large gap and an inner ring producing the bulk of the emission (in H and K-bands) close to 0.1 AU is able to account for all the observations. With this study, the presence of an optically thick inner dusty disk close to the star and dominating the H and K- bands emission is confirmed. According to our model, the large gap extends up to ~ 7.5 AU. This points toward a companion (located at several AU) gap-opening scenario to explain the morphology of T Cha.