Potters chairman Peter Coates has confirmed the club's interest in the former Manchester United man, whose agent has held meetings with the Premier League outfit
Diouf joined Hannover in January 2012 after two-and-a-half frustrating seasons with Manchester United, and scored 27 goals in 51 games for the Bundesliga club, but the 25-year-old striker is now entertaining a possible transfer.
The German club's sporting director, Dirk Dufner, confirmed on Friday that Diouf's agent, Jim Solbakken, has been in contact with Stoke.
"I phoned Jim in the morning and he told me that he has met with Stoke," Dufner told Bild.
Stoke chairman Peter Coates also confirmed Diouf is a transfer target as new manager Mark Hughes begins to put his stamp on his squad.
"He is one of the strikers we have registered an interest in," Coates said.
Diouf joined Manchester United in July 2009 after an impressive stint with Norwegian club Molde, but only managed five appearances under Sir Alex Ferguson and scored one goal, before spending time on loan in Norway and with Blackburn Rovers.
Dufner has denied Hannover have received any official bids and remains confident they may still be able to convince the forward to stay.
"At the moment, Mame will not sign [a new contract]," Dufner said. "It is not bad if he waits for the end of the transfer period [and] then signs just after 31 August."