The former Manchester United player is thought to be a long-term target for Stoke boss Mark Hughes and he appears to have finally landed the Senegal international.
Diouf's current deal is set to expire and he has been offered a second chance to shine in English football after a difficult spell at Old Trafford where he made only a handful of first-team appearances.
The 26-year-old spent a loan period at Blackburn, but sought out a fresh start in Germany after failing to hold down a regular role with United.
He scored eight goals for Hannover last season and Hughes is keen to add more firepower to his squad at the Britannia Stadium.
Stoke are also thought to have held preliminary talks with Monaco about striker Emmanuel Riviere.
The Frenchman has attracted interest after scoring 10 times for the Ligue One side and reports suggest a deal would cost around £5m.
It has been a busy start to the summer for Stoke, who have already secured the signing of Sunderland defender Phil Bardsley on a three-year deal.