Xhaka was instrumental as Sunderland finished seventh in the Premier League last season on their return to the top flight, driving the club's qualification for the Europa League.
Chelsea's new manager Xabi Alonso had been keen to reunite with the 33-year-old following a successful spell together at Bayer Leverkusen, and the Swiss international was reportedly attracted by the prospect of working with him again. But after discussions with Sunderland, Xhaka reaffirmed his commitment to the Stadium of Light.
"No, this topic is closed," Le Bris said when asked about Xhaka's future.
"He has been really clear about his future. He loves Sunderland, he wants to stay in Sunderland. He wants to make the future of Sunderland. He is a good captain. A great leader."
Xhaka's rapport with Sunderland's supporters and his connection to the club also played a part in his decision to snub Chelsea's interest and continue his spell on Wearside, having joined from Leverkusen for around £17 million last summer.
Sunderland's transfer business this summer is likely to look very different from last year's overhaul, when the club signed 14 players following promotion from the Championship. So far they have made just one addition, bringing in experienced full-back Thomas Meunier on a free transfer from Lille, and Le Bris has urged patience among supporters expecting further reinforcements.
"It's going to be quiet. Under the radar, right? Because I think we are working hard behind the scenes, and it's really important to be quiet because otherwise, it's a mess," Le Bris said. "And we are looking at probably a different transfer window if you compare with last season.
"We had to sign 14 new players. That won't be the case this year. We'll see what will happen."
The comments came after Sunderland's 4-2 pre-season defeat to Liverpool in Nashville, in which the Black Cats gained further valuable minutes on their US tour, with Le Bris continuing to build fitness and cohesion ahead of the new Premier League campaign without needing to overhaul the squad as dramatically as 12 months ago.
Xhaka's importance to Le Bris's project extends beyond his performances on the pitch, with the captain a central figure in the dressing room and a key voice helping the squad's younger players settle into Premier League life.
His experience winning the Bundesliga title and reaching a European final under Alonso at Leverkusen made him an obvious target for Chelsea's new manager, but Sunderland's refusal to even entertain a fee well below his valuation reflects how central he has become to the club's plans on and off the pitch.
With the captain's future now settled, Le Bris's comments suggest the club will continue working quietly on potential incomings rather than pursuing the kind of high-volume rebuild seen last summer, prioritising continuity in a squad that already overachieved expectations in its first season back in the top flight.