The 33-year-old has been subject to an £8 million bid from Chelsea earlier in the summer, at the request of new boss Xabi Alonso.
Sunderland turned it down out of hand, deeming it ‘insulting’ and Xhaka reaffirmed his commitment to the club.
Xhaka is contracted to the club until 2028 and played a key role in Sunderland qualifying for Europe last season, scoring once and providing six assists in his 34 league games.
Speaking to reporters after Sunderland’s 4-2 pre-season loss to Liverpool, Le Bris confirmed that Xhaka will not be joining up with his former manager.
"No, this topic is closed. He has been really clear about his future. He loves Sunderland, he wants to stay in Sunderland,” he said.
“He wants to make the future of Sunderland. He is a good captain. Great leader."
Le Bris also said that he’s expected a “quiet” summer for Sunderland, adding: "It’s going to be quiet. Under the radar, right? I won’t give you information.
“Because I think we are working hard behind the scenes, and it’s really important to be quiet because otherwise it’s a mess.
“And we are looking at probably a different transfer window if you compare with last season. We had to sign 14 new players. It won’t be the case this year. We’ll see what will happen."