The 23-year-old had been widely expected to join the Premier League leaders this January with the expectation that he would be sent on loan to Vitesse Arnhem on loan until the end of the season.
Nigel Pearson is desperate to sign a new striker this month after watching his Foxes side slump to the bottom of the table.
Reports have linked them with a move for Jermain Defoe but the former England star's wages have proved too tall a hurdle for them to jump.
Kramaric, on the other hand, initially hoped to sign for Chelsea this January and play out the rest of the season on loan at the King Power Stadium but top flight rules prevent clubs from such a move.
The temptation of playing Premier League football immediately, however, rather than waiting until the new campaign, appears to have swayed the HNK Rijeka striker into opting for life in the East Midlands.
The in-demand Croat has scored a stunning 28 goals in all competitions for his club this year while also notching two goals in four appearances for the national side.
Leicester, who are also close to announcing a deal for Blues goalkeeper Mark Schwarzer, hope to agree personal terms this evening while a medical is expected to be completed in the morning.
Jose Mourinho wished 42-year-old Schwarzer well after his side's comfortable FA Cup victory over Watford at the weekend.
"I want to publicly thank Mark Schwarzer because he's leaving us and he was a fantastic guy for us," said Mourinho.
"As a goalkeeper, when we needed him he was there for us, and as a person and a professional he was an amazing guy in our group.
"On behalf of myself, my staff and my players I want to say we are going to miss the big guy and we wish him all the best in his new life at Leicester."
After Esteban Cambiasso joined Danny Drinkwater, Dean Hammond and Andy King on the treatment table, Pearson may be in the market for a central midfielder too with only Matty James currently available for selection.
When asked if he would like to share his plans for the January window after the 1-0 victory over Newcastle, Pearson simply replied: "No."
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