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The Universe is not perfectly homogeneous, the large scale structure formsoverdense regions and voids. In this paper, we consider the possibility that weoccupy a special position in our Universe, close to the center of a localunderdense region that we model as an LTB void embedded in a homogeneous andisotropic Universe. The CMB sky measured by an off-center observer in this voidis not statistically isotropic. In addition to the non-stochastic CMBanisotropies due to the geometry of the model, we also observe a lensing-likedistortion of the CMB anisotropies. In this article, we propose a framework toforecast the precision with which we can measure the amplitude of thelensing-like deformation of the CMB temperature anisotropies. For illustrativepurposes, we apply this method to a couple of large-scale void models differingover the matter density profile and we show that the CMB temperature data fromthe Planck satellite is potentially capable to detect the effect for the largevoids chosen here. A companion paper will be dedicated to a systematicexploration of different realistic void models.

CMB sky for an off-center observer in a local void I: framework for forecasts