The Switzerland midfielder, whose contract runs until 2028, was attracted by the prospect of reuniting with Chelsea manager Xabi Alonso, having played under him at Bayer Leverkusen.
Chelsea had an £8 million bid for Xhaka rejected by Sunderland last week, and the Blues were expected to return with an improved offer.
Sources at Sunderland have told BBC Sport, however, that the 33-year-old is not for sale.
Following discussions, Xhaka has reaffirmed his commitment to the Black Cats.
Chelsea have not given up hope of landing Xhaka.
Sources at the club maintain that the former Arsenal midfielder remains keen on a move to Stamford Bridge. It remains to be seen whether the Blues will submit a further bid.
Xhaka helped Sunderland qualify for Europe for the first time in 53 years last season following his arrival from Bayer Leverkusen.
He made 34 Premier League appearances as the Black Cats finished seventh to secure Conference League qualification.
The Switzerland captain spent seven years at Arsenal, making 297 appearances, before joining Leverkusen in 2023, where he helped the German club win their first Bundesliga title under Alonso.
Xhaka is currently at the World Cup in the United States, Mexico and Canada with Switzerland, where he has played every game in his country's run to the last 16.