Leicester have turned down a £15million bid from Ligue 1 side Monaco as they look to recoup more of the £23m they forked out for the midfielder.
Boubakary Soumare joined Leicester only last summer but Brendan Rodgers is willing to allow him to leave to generate funds to refresh his squad.
Leicester are the only Premier League club still to make a signing this summer, and Orkun Kokcu of Feyenoord is one of Rodgers primary targets.
Soumare shone as Lille won the Ligue 1 title in 2020-21 but the midfielder struggled to adapt to life in England, starting only 18 games across last season.