The 26-year-old Scotland international is currently playing at Euro 2020, as his side prepares for a do-or-die group game with Croatia on Tuesday.
According to the Daily Mail, Christie has not committed to a new contract with Celtic, which means this summer may be the club's final chance to get a fee for his signature.
Despite failing to secure Odsonne Edouard from Celtic, it appears Leicester will push to try and Christie from the Scottish giants.
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