Coach Patrick Mouratoglou’s main focus is on Serena Williams. But he can’t help but keep tabs on Coco Gauff.

Mouratoglou met Gauff when she was 10 years old. The family decided to have Gauff, from Delray Beach, Fla., train intermittently at the Mouratoglou Tennis Academy in the south of France, near Nice.

That the Gauff camp was interested in flying Coco to France to hone her craft speaks volumes to Mouratoglou’s stature. The coach, who also does analyst work for ESPN, set up a game plan for Coco that has proved successful.

Coming off her run to the fourth round at Wimbledon, upsetting Venus Williams along the way, Gauff will make her U.S. Open debut Tuesday against 77th-ranked Anastasia Potapova. It will be the third match on Louis Armstrong Stadium.

The American is ranked 139th and received a controversial wild card into the main draw here from the USTA despite it exceeding her limit of three wild cards set for 15-year-olds.

“I saw a future champion,” Mouratoglou told The Post in a players’ lounge interview Sunday. “Everything I believed was necessary to become a champion, I can see at that age already. If I point out the most important things, saw athleticism, the drive, self-confidence — but not cocky — just a belief in herself. Hard worker. Super competitor. You see her in practice, then she goes into the match, it’s a different level. She knows how to win.”

With a full-time commitment to Serena, Mouratoglou cannot be Coco’s coach. Perhaps after Serena retires.

The current job belongs to Coco’s father, Corey. Mouratoglou arranged for a secondary coach in fellow Frenchman Jean-Christophe Faurel, from his academy. Coco’s mother, Candi, is a former Florida State hurdler and got her daughter into tennis in the second grade.

“We provided a good environment,” Mouratoglou said. “She has a great family who have a big role. She looks up to her father the most. They had other needs. They needed a fitness plan, hitting partners and establishing a long-term plan.”

And now Gauff is fulfilling her potential — earlier than expected, even though she became the youngest U.S. Open junior finalist in 2017 at age 13. At Wimbledon, she became the youngest qualifier in history and youngest player to make the fourth round since Jennifer Capriati in 1991.

“Yes and no,” Mouratoglou said when asked if he was surprised. “Yes, you can’t expect something like that at that age. On the other hand, she made history many times with her young age.’’

Gauff has tried to avoid the spotlight in the buildup to the Open, declining to go to media day. She stopped in on Arthur Ashe Kids’ Day on Saturday and belted balls into the stands.

“She continues to deal well with pressure and that’s something very rare,’’ Mouratoglou said. “It’s one more quality you can’t see when she’s 10 but you started to see it at 12, 13.”

A third-round meeting against defending champion Naomi Osaka looms. Duplicating Wimbledon’s journey into the fourth round will be a tough task.

“Why limit her?” Mouratoglou said. “Bad luck [getting] Osaka, but bad luck for who?

“I think she could do well but it’s no pressure because everything’s new. The attention she got was unreal after Wimbledon. You always need time to get used to the new status and so many changes. With her, she is often very surprising. That’s why she’s exciting.”

ESPN’s Chris Evert cautioned about expecting too much, too soon.

“Coco Gauff had one fantastic tournament, at Wimbledon,” Evert said. “I hope we’re not putting too much pressure on her. But looking at her game, she has everything skill set-wise as far as power and touch and variety of shots.”