The Gaia mission has been designed to perform absolute astrometric measurements with unprecedented accuracy; the end-of-mission parallax standard error is required to be of the order of 10 μ as for the brightest stars (V≤ 10) and 30 μ as for a G2V-type star of magnitude 15. These requirements set a stringent constraint on the accuracy of the estimation of the location of the stellar image on the charge-coupled device (CCD) for each observation: e.g. 0.3 mas or 0.005 pixel for the same V= 15 G2V star. However, the Gaia CCDs will suffer from charge transfer inefficiency (CTI) caused by radiation damage that will degrade the stellar image quality and may degrade the astrometric performance of Gaia if not properly addressed. For the first time at this level of detail, the potential impact of radiation damage on the performance of Gaia is investigated. In this paper (first of a series of papers), we focus on the evaluation of the CTI impact on the image location accuracy using a large set of CTI-free and damaged synthetic Gaia observations supported by experimental test results. We show that CTI decreases the stellar image signal-to-noise ratio and irreversibly degrades the image location estimation precision. As a consequence, the location estimation standard errors increase by up to 6 per cent in the Gaia operating conditions for a radiation damage level equivalent to the end-of-mission accumulated dose. We confirm that, in addition, the CTI-induced image distortion introduces a systematic bias in the image location estimation (up to 0.05 pixel or 3 mas in the Gaia operating conditions). Hence, a CTI-mitigation procedure is critical to achieve the Gaia requirements. We present a novel approach to CTI mitigation that enables, without correction of the raw data, unbiased estimation of the image location and flux from damaged observations. We show that its current implementation reduces the maximum measured location bias for the faintest magnitude to 0.005 pixel (∼4 × 10−4 pixel at magnitude 15) and that the Gaia image location estimation accuracy is preserved. In the second paper, we will investigate how the CTI effects and CTI-mitigation scheme affect the final astrometric accuracy of Gaia by propagating the residual errors through the astrometric solution.