The centre forward wants one more crack at the Premier League before he retires.
Vardy, who is now 37, scored two in a 3-0 win over Preston to seal promotion.
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Foxes boss Enzo Maresca has got his wish to retain Vardy, per The Sun and other sources.
He will put pen to paper on an extension and move into his 13th year at the club.
Vardy emerged from the lower leagues of English football to become a league title winner.