N'Diaye will now discuss personal terms with Martin O'Neill's side after a fee - believed to be around £3m - was agreed with Turkish side Bursaspor.
The French U21 midfielder, who can also play at centre-half, started his career with Nancy before leaving for Turkey in 2011.
N'Diaye will be a welcome boost for O'Neill's threadbare squad after the Sunderland boss was only able to name six substitutes in last weekend's FA Cup game with Bolton.
Meanwhile, defender Blair Adams has extended his loan spell with Coventry City.
The 21-year-old initially joined the Sky Blues in November and will remain at the Ricoh Arena until 16 January.