Real are said to be scouting the Spaniard this season.
Agent Alejandro Camano told Sportitalia: "He can be one of the best central defenders in the world, he is very young, he has a great personality and a hard worker.
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"He is absolutely ready to make the Lazio fans happy. Then he will play wherever he wants, because he is ready to be number one."
Gila was sold by Real to Lazio in 2022 and the Spanish giants maintain a buy-back option in the deal.