Valencia are hoping to secure the forward back on loan, after he impressed there at the back end of last season.
Spanish outlet Super Deporte states that Conte has a specific stance on Gil that is not negotiable.
He will keep the youngster until the club can secure him a replacement in the squad.
If Spurs sign another player, then Gil is free to go out on loan for regular game time.
The youngster has only managed 73 minutes in all competitions so far this season.