The Foxes have reportedly offered £3.7 million for the Hajduk Split midfielder, but face competition for his signature.
Last week, HITC Sport brought you the news that the Bosnian midfielder was being targeted by a host of Premier League clubs as he looks to seal a move to England.
Now, Leicester have apparently made the first move to secure the defensive midfielder ahead of their rivals.
The Foxes have reportedly offered £3.7 million for the 23-year-old, with his current club thought to want that at a minimum before they will sell their prize asset, according to the Mirror report.
Stoke have also been keeping track of the player since last summer, and could now make their move as well.
Either side would be confident of securing him as well, with the player reportedly keen on a move to England ahead of one to Europe, despite interest from Italy, France and Spain.
Claudio Ranieri has already signed winger Demarai Gray from Birmingham, and he is keen to keep strengthening to maintain their push at the top of the table.
The Bosnia international could be a replacement for Gokhan Inler, who could leave in January after failing to establish himself in side since joining in the summer.