Gila was one of the best players in Lazio's victory against AC Milan on Sunday.
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Milan are among the clubs interested in signing him, with Atlético Madrid and Inter Milan also interested.
Real Madrid are waiting in the wings, as they own 50 per cent of the player's registation.
Defensive partner Patric said after yesterday's win: "He's growing tremendously, he has impressive physical qualities; you don't see players that fast in that area of the field.
"I hope he continues like this, but I'm not going to talk about the future; that's his business. He needs to keep a cool head, stay focused, and never talk to us about the future."