Gago was carried off on a stretcher during Argentina's 1-1 draw in a World Cup qualifier in Peru and the player tipped to be a central figure in new coach Mauricio Pellegrino's plans has missed Valencia's last three games.
Pellegrino bought his compatriot from Real Madrid in July after the midfielder had spent last season on loan at AS Roma and found himself surplus to requirements at the Bernabeu.
Another Argentine, the accident-prone Ever Banega, also returned to training with the rest of the squad after recovering from a broken ankle sustained when his car rolled back over his leg after he failed to set the handbrake in a petrol station.
Valencia have made a poor start to the season and lie 15th in La Liga with five points from five games.
They also lost 2-1 at Bayern Munich in their opening game in Champions League Group F.