Reports have suggested that Potters officials have been in Germany to discuss a possible deal for the former Manchester United striker.
Diouf, who has impressed since leaving England for the Bundesliga, has entered the final year of his contract and Stoke were hoping to land him without shelling out big money.
They may, however, be forced to wait until next summer before rekindling their interest, with Hannover making it clear that they have no need to cash-in on the 25-year-old.
Club president Martin Kind told Bild: "We do not need the money. His goals may be more important for us.
"If Stoke offered 20 million euros, then we'd think about it, but I don't think that is realistic."
Hannover's director of sport Dirk Dufner added: "It looks like he'll be staying with us.
"He is a good boy and an absolute professional, who has exerted no pressure on the club."