Zlatko Dalic's side became national heroes as they reached the World Cup final, only to fall to a 4-2 defeat to France in Moscow.
However, Kalinic has seemingly rejected the chance of a priceless souvenir of the occasion, having been sent home after just one game of the tournament.
It was claimed that the AC Milan striker refused to come on as a substitute during Croatia's 2-0 win against Nigeria, citing a back problem.
Dalic claimed the striker had done likewise in a warm-up game against Brazil and a training session and promptly ended the striker's stay, insisting he needed all of his players fit and ready to play.
The Croatian press reported that Kalinic's response to the offer of a medal was simply: "thank you but I did not play in Russia."