The 24-year-old only completed his move from Croatian outfits Rijeka for a record-breaking £9million during the previous January window, but has so far struggled to hold down a regular role.
Kramaric has been unable to overtake star striker Jamie Vardy to a spot up top, with second choices Leonardo Ulloa and Shinji Okazaki also preferred ahead of him in the pecking order.
The Hammers are currently struggling with injuries in their forward line as Diafra Sakho is still unavailable while Andy Carroll looks to have picked up another knock in 3-1 win over Bournemouth yesterday.
Foxes boss Claudio Ranieri is also believed to be open to allowing the Croatia international to leave the King Power Stadium given his lack of playing time.
He is yet to register a single Premier League start for his side this term, so far featuring only two times as a substitute.