Black Cats officials flew to Turkey with an improved offer after their initial bid, said to be in the region of £2million, was turned down.
The combative tough-tackling 21-year-old N'Diaye started his career with French club Nancy before moving to Bursaspor in July 2011.
N'Diaye is believed to be flying to the north east for a medical and to discuss personal terms. If confirmed, he will become boss Martin O'Neill's first signing of the January transfer window.