Eight-time champion Federer reached the Wimbledon fourth round for the 17th time on Saturday, becoming the first player, man or woman, to record 350 Grand Slam match wins.

In the second week, he will be joined by longtime rivals Rafael Nadal and Novak Djokovic.

Gauff will also be there in the women's event -- the youngest to progress this far since US compatriot Jennifer Capriati in 1991.

Federer sees no reason why world number 313 Gauff cannot take the title.

"I don't see a reason why younger women players should run into physical issues or not win tournaments young," said Federer.

"I think it's possible. She seems developed. She's moving great. I think it's one of her great strengths.

"And her mind. I was terrible at 15. Couldn't be on a court for longer than an hour and a half. I would walk away."

Nadal was the last teenage man to win a Slam title when he defeated Federer on his 19th birthday in the final of the 2005 French Open.

Federer was 21 when he captured his maiden Slam at Wimbledon in 2003 while Djokovic was 20 when he claimed his first major at the 2008 Australian Open.

"I think on the men's side, maybe at 15 it's not possible, I don't think, to go through a Slam," added Federer.

"At 17 and 18, what Rafa did or (Boris) Becker did or (Bjorn) Borg did, I think it's possible.

"I do believe the depth is bigger on the men's... side, so you need to beat better players every round, whereas maybe in the past I don't think the depth was as great."

On Saturday, Swiss second seed Federer eased past French 27th seed Lucas Pouille 7-5, 6-2, 7-6 (7/4) and will face Italy's 17th seed Matteo Berrettini for a place in the quarter-finals.

Federer's 17th appearance in the fourth round at Wimbledon takes him ahead of Jimmy Connors on the all-time list.

"The records mean something to me, but not everything just because I am very much aware that not everybody for the last hundred years played all the Slams," admitted the 20-time major winner of his 350-win landmark.

"It's really only the last 20 years that that's been going on," he said, explaining that not all players could travel to all four majors in the past.

"I'm sure that's going to keep happening from now on, most of the players will keep playing."

Berrettini saved three match points to see off Diego Schwartzman of Argentina 6-7 (5/7), 7-6 (7/2), 4-6, 7-6 (7/4), 6-3.

The 23-year-old Italian will be playing in his first last-16 at the Slams.