The Argentine has been impressed by his compatriot, but has called on him to get in shape ahead of the new campaign in order to keep up with the pace of Los Che's game
The 40-year-old, who was appointed Los Che's new coach back in May after Unai Emery parted company with the club, bought Gago from Real Madrid for a reported €3.5 million earlier in July.
The Argentine midfielder joined his new team-mates for their recent three-match pre-season tour of Germany, and his compatriot is impressed by what he has seen so far.
"Fernando has an eye for a good pass, and he moves well around the pitch, his positioning is excellent," Pellegrino said.
But the coach, who turned out for Valencia between 1999 and 2005, believes that the player needs to improve his stamina.
"He needs to keep playing to be able to live with the pace of the game. We have not rested a single day and we hope that the intense workload will improve Fernando's fitness."
Los Che continue their pre-season campaign against Porto on Saturday.