Gil arrived at Tottenham last summer from Spanish giants Sevilla but struggled for game time in the Premier League.
Spurs boss Antonio Conte allowed the winger to return to his homeland in January where he impressed on loan for Valencia, back in La Liga.
Los Che have been keen on having Gil back at the club this season, while Tottenham are open to letting him leave in the ongoing window.
Valencia coach Gattuso has made it a priority to re-sign Gil and the player is also keen on the move.
The Italian has confirmed that his side are working on signing Gil and stressed he is hoping a deal for him could be wrapped up next week.
“I like Bryan Gil, I like players that look to play football”, Gattuso told a press conference while discussing Valencia’s intentions to sign Gil.
“We are working on it.
“Next week we will fix the problems that we have.”
The Spaniard also has ambitions to represent his country in the upcoming World Cup and a move back to Valencia, where he is likely to get regular game time, could aid him in his cause.
