The Senegalese striker, who represented his country at this summer's World Cup finals in Russia, scored six Premier League goals last season as Stoke were relegated to the Championship.
Leicester's current bid does not meet the Potters valuation however, which as reported by The Sun, stands at around £15m.
The Foxes have been tracking Diouf's progress over the last three transfer windows and could make an improved bid for the forward before the transfer deadline on Thursday afternoon. The forward was an unused substitute for Gary Rowett's side in their opening Championship game, a 3-1 defeat to Leeds United on Sunday afternoon.
Claude Puel's team still have funds to strengthen their squad after selling Riyad Mahrez to Manchester City for £60m earlier this summer. Puel has spent most of that money on new arrivals, bringing in the likes of Norwich City's James Maddison, FC Porto defender Ricardo Pereira and winger Rachid Ghezzal from Monaco.
Despite spending big, Puel could still look to bring Diouf in to compete with Jamie Vardy, Kelechi Iheanacho and Fousseni Diabaté for a starting role next season, with Shinji Okazaki currently out injured and Islam Slimani looking set for a King Power Stadium exit.
Diouf joined Stoke in 2014, scoring 11 Premier League goals in his first full season at the bet365 Stadium. However, he has only managed to score 12 league goals in the past three seasons, with half of them coming in Stoke's dismal campaign last season where they suffered relegation from the top-flight.
The 30-year-old started his career at Norwegian side Molde, scoring 45 goals in 86 appearances in all competitions which earned him a move to Sir Alex Ferguson's Manchester United. He only made nine appearances at Old Trafford and despite a decent loan spell at Blackburn Rovers in 2011, moved to Hannover 96 at the start of 2012.
There, Diouf scored 35 goals in 71 appearances for the Bundesliga side, subsequently earning himself a move back to the Premier League with Stoke four years ago.
The Foxes will need to act quickly if they want to sign Diouf, with the transfer window closing earlier than usual this season, at 5pm on August 9.