Nico left Camp Nou on loan in search of regular minutes in August but has struggled to nail down a first-team spot with Valencia.
Although Valencia have made a decent start to their first campaign under Gattuso, winning four of their first eight LaLiga games, the 20-year-old has played a limited role.
Nico has made seven league appearances this season, but five of those outings have come from the bench, meaning he has featured for just 231 minutes in the competition.
With Barcelona enduring an injury crisis, reports in Spain have suggested the Blaugrana could cut Nico's loan short in January, but Gattuso has called for him to force his way into Valencia's team instead.
"This is the first time I've heard of it. No player has spoken to me," Gattuso told reporters on Friday. "He is working very well. He has a one-year contract with us. The player has not come to talk to me.
"All the players want to be starters and I think he should work well on the field, and when he has the opportunity to play, show it.
"He is a great professional. He trains very well but I have a squad of 23 or 24 players. He is a kid who always trains fully."
Lorenzo Insigne scored the only goal of the game from the penalty spot after Giorgio Chiellini caught Amir Rrahmani in the face with a flailing arm.
That was one of only two shots on target Napoli managed in Saturday's 1-0 win at Estadio Diego Armando Maradona, compared to six for Juve - five of those in the second half.
And Pirlo, who saw Juve lose for the second time in five league matches to drop more points in the Scudetto race, felt his side were hard done by.
"They barely had a shot on goal and we lost through a dubious decision," he told Sky Sport Italia. "We played a good game but did not get the result we deserved.
"We played the ball around but not quickly enough, allowing Napoli to get back. We created more chances in the second half but did not find the goal."
Asked to elaborate on why he considered the 31st-minute penalty to be dubious, Pirlo said: "If you give a penalty for that then any contact in the box is punishable.
"If that had been given for us there would have been a lot of controversy and complaints, though I don't know if we would have been given a penalty in a situation like this."
Juventus have had five penalties in Serie A this season, putting them level with Roma and Sassuolo and behind only Milan, who have had an incredible 14.
Alex Meret, a late addition to Napoli's starting line-up after David Ospina sustained an injury in the warm-up, made six saves to frustrate Juve in front of goal.
Cristiano Ronaldo had four on-target shots kept out, while Alvaro Morata had a goal disallowed for an infringement by Chiellini - making his 400th Serie A outing - in the build-up.
But rather than blame his attackers for firing a blank, Pirlo instead credited Meret for standing firm between the sticks.
"My players played the game they had to," he said. "It is normal that playing so many games close together means a loss of sharpness.
"But both those who started and came on from the bench had an excellent game. The only thing lacking in the end was a goal.
"There's no guarantee the team that scores the most goals then wins the Scudetto.
"We create plenty of chances and the Napoli goalkeeper was man of the match, so I can't complain about my strikers today."
Napoli's victory was their first in four matches and eases the pressure on boss Gennaro Gattuso, who was reportedly set to be sacked had his side lost again on Saturday.
However, Gattuso - a former team-mate of Pirlo's for club and country - insisted he never doubted the backing of his players and staff.
"We showed great heart and determination," he said. "Juve deserved something more, but my team was under pressure and fought hard to keep the clean sheet.
"I never had doubts on this squad, otherwise I would've packed up my things and gone home.
"You can't get anywhere without the faith of the players. I always felt they were ready to do what I asked and that’s what matters."
The former Milan and Napoli coach was appointed ahead of the 2022-23 season after a year out of the game.
But Gattuso has been unable to inspire Valencia, who finished ninth last term.
Gattuso leaves the club in 14th place, winless in four outings since the World Cup break and just a point above the bottom three – albeit with a game in hand over the other sides in the bottom half.
Following Sunday's last-gasp defeat to Real Valladolid – his final match at the helm – Gattuso addressed supporters and told them Valencia's poor results were his responsibility.
The 45-year-old also angrily confronted the assembled media a day before Valencia announced his exit.
"Valencia CF announce that this Monday, January 30th, the club and the first team coach, Gennaro Gattuso, have decided by mutual agreement to end the contractual relationship between the two parties," a statement read.
"The club wish to thank Gattuso for his commitment and work during his time in charge and wish him the best of luck for the future.
"The team will return to training this Tuesday, January 31st, under 'Voro' Gonzalez."
Voro, who is set to take charge of the team at Real Madrid on Thursday, is in his seventh spell as interim coach, having also led Los Che on a permanent basis in the second half of the 2016-17 campaign.
