Roma are also battling to sign Soule, who can play in a variety of positions across forward areas, but Leicester are now understood to be in the driving seat.
Cooper was appointed last month as Leicester’s new head coach after the departure of Enzo Maresca to Chelsea, and has already made a number of signings.
After the £30 million sale of Kiernan Dewsbury-Hall to Chelsea, Cooper has already sealed the capture of former Fulham forward Bobby De Cordova-Reid and Chelsea’s teenage midfielder Michael Golding.
Okoli has also been recruited while Leicester have completed the £14 million capture of Abdul Fatawu, who was on loan last season from Sporting.
Another forward is thought to be a priority, with Cooper looking for an alternative option to Jamie Vardy, Tom Cannon and Patson Daka.
Leicester kick off their Premier League season at home to Tottenham on August 19.
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