The 38-year-old was powerless to stop Leicester from being relegated last season, departing after 13 successful years at the club.
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Vardy has no intention of calling time on his impressive career, and, according to The Sun, he has his heart set on a move to Celtic.
Rogers is also understood to be keen on a reunion with his former striker but will face competition from other clubs.
The report adds that Vardy believes he can compete at the highest level for up to two more seasons West Ham, Brentford, and Championship side Wrexham have also been linked.