Leicester have had a bid for Mame Biram Diouf rejected by Stoke after the 2015/16 Premier League champions failed to meet a £15million valuation.
The Foxes previously had another bid for the Senagalese striker rejected after failing to meet the demands of Stoke, who began their Championship campaign on Sunday.
The 30-year-old - who joined Stoke four years ago on a free transfer from German club Hannover 96 - has been a target for Leicester during the past three windows, according to The Sun.
The forward featured in two games for Senegal at the recent World Cup finals in Russia and has made over 120 appearances for Stoke, netting on 23 occasions.
However, Diouf was an unused substitute in Stoke’s 3-1 defeat to Leeds on Sunday in their first Championship game of the season.
Leicester boss Claude Puel has funds available after the sale of Riyad Mahrez to Manchester City went through last month for £60m.
The Frenchman has already signed James Maddison from Norwich for £20m, as well as bringing in Ricardo Pereira, Jonny Evans and Danny Ward.
Only on Sunday, Monaco winger Rachid Ghezzal joined the King Power Stadium on a four-year deal, becoming the fifth signing of this summer transfer window.
Leicester only have four days remaining until the transfer window closes, with a 5pm deadline on Thursday.