Mali have made another attempt to persuade N'Golo Kante to pledge his future to the West African country.
The uncapped 24-year-old could represent France, where he was born, or his parents' birthplace Mali.
Kante, who opted not to join Mali at the 2015 African Cup of Nations, has been superb for Leicester this season.
"It's impossible to overlook a player of such quality and we've already approached his representatives," Mali boss Giresse said.
"Kante will add a lot to any country but my big hope is that it will be the national team of Mali."
Although Kante previously rejected Mali, the offer came during his first season in the French top-flight while he was playing for Caen and he said at the time he was not ready for international football.
But he also suggested he would play for Mali in the future.
Since joining Leicester in a £5.6m deal last summer, Kante has been an ever-present for the Foxes and a major factor in the team's thrilling rise to the Premier League summit.
He has made 25 appearances for the league leaders in all competitions this season, scoring once and providing two assists. He has also made the most interceptions (87) and won the most tackles (63) in Europe's top five leagues this term.