Leicester have been hoping to sign M’Baye Niang this month.
The Foxes have been searching all month to bring striker cover to the King Power Stadium, but have so far found their advances rebuffed by a number of teams.
Niang is their latest target, and Claudio Ranieri is keen to bring the French Under-21 international to the club as a preparation for next season.
He submitted a formal bid of roughly £12.2 million (€16m) for Niang, aware that his youth, reputation and versatility in the final third make him an expensive asset.
The offer was staggered to include potential bonuses should Leicester qualify for the Champions League, buy Milan quickly rejected the approach for a player who has been on their books since 2012.
He has spent various loan spells away from the San Siro, but has started making an impact upon the Milan first-team again this season, playing all of the last 10 games having started the campaign injured.
His form has not been outstanding, but Milan clearly rate the youngster highly, and they are refusing to sell him for the fee submitted by Leicester.
It is not stated in the report as to whether Leicester are ready to submit another approach for Niang.