There is some concern that the striker does not meet the necessary criteria to gain the work permit, and a hearing is scheduled for next week.
Chelsea were also reported to be interested in signing Kramaric, but the 23-year-old may be heading to the other end of the table to the King Power Stadium.
Leicester, who are lying bottom of the Premier League, currently have the likes of Leonardo Ulloa, David Nugent and Jamie Vardy as options in attack.
Kramaric joined Dinamo Zagreb as a six-year-old and made his debut at the age of 17 in 2009 before being shipped out on loan to Lokomotiva Zagreb, where he averaged nearly a goal every two games.
When Kramaric’s return to Dinamo hit the rocks, Rijeka were quick to step in and secure his services in August 2013 – signalling the start of the most fruitful period in the striker’s career and resulting in a full senior debut for Croatia.