Potters chairman Peter Coates has confirmed that the former Manchester United forward is 'one of the strikers we have registered an interest in'.
Mark Hughes has turned his attention to the Senegal international after seeing him net 27 times during 18 productive months in Germany.
Diouf would have no problem adjusting to life in the Premier League should he move to the Britannia Stadium, having also turned out for Blackburn Rovers during a loan spell in 2010/11.
Hannover, though, are reluctant to part with the 25-year-old frontman.
Sporting director Dirk Dufner concedes that Diouf's representative has opened talks with Stoke, but insists there is no guarantee that a deal will be done.
He told Bild: "I see the opportunities still not bad.
"At the moment, Mame will not sign.
"It is not bad if he waits for the end of the transfer period, then signs just after 31st August."