Context. A key objective of the ESA Gaia satellite is the realization of a quasi-inertial reference frame at visual wavelengths by means of global astrometric techniques. This requires accurate mathematical and numerical modeling of relativistic light propagation, as well as double-blind-like procedures for the internal validation of the results, before they are released to the scientific community at large. Aims. We aim to specialize the time transfer functions (TTF) formalism to the case of the Gaia observer and prove its applicability to the task of global sphere reconstruction (GSR), in anticipation of its inclusion in the GSR system, already featuring the Relativistic Astrometric MODel (RAMOD) suite, as an additional semi-external validation of the forthcoming Gaia baseline astrometric solutions. Methods. We extended the current GSR framework and software infrastructure (GSR2) to include TTF relativistic observation equations compatible with Gaia’s operations. We used simulated data generated by the Gaia Data Processing and Analysis Consortium (DPAC) to obtain different least-squares estimations of the full (five-parameter) stellar spheres and gauge results. These were compared to analogous solutions obtained with the current RAMOD model in GSR2 (RAMOD@GSR2) and to the catalog generated with the Gaia RElativistic Model (GREM), the model baselined for Gaia and used to generate the DPAC synthetic data. Results. Linearized least-squares TTF solutions are based on spheres of about 132 000 primary stars uniformly distributed on the sky and simulated observations spanning the entire 5 yr range of Gaia’s nominal operational lifetime. The statistical properties of the results compare well with those of GREM. Finally, comparisons to RAMOD@GSR2 solutions confirmed the known lower accuracy of that model and allowed us to establish firm limits on the quality of the linearization point outside of which an iteration for non-linearity is required for its proper convergence. This has proved invaluable as RAMOD@GSR2 is prepared to go into operations on real satellite data. Key words: astrometry / gravitation / methods: data analysis / space vehicles: instruments⋆ Present address: Astronomical Institute, University of Bern, Sidlerstrasse 5, 3011 Bern, Switzerland.