The veteran forward has entered the final year of his Leicester contract and his future remains unclear following the club's relegation to the Championship.
Vardy is yet to hold talks over his future with new boss Enzo Maresca since he took charge of the club.
However, according to Sky Sports News, the 36-year-old has taken the decision not to join the Saudi Pro League because he does not think it would suit his family.
Vardy is a Leicester legend having spent 11 years with the club and playing a key role in their Premier League title success and subsequent journey into the Champions League.
The striker has bagged 136 top-flight goals for the Foxes, but his contribution was limited to just six goals in 42 appearances last term.
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With Leicester having lost stars including Youri Tielemans and James Maddison this summer, Vardy's leadership could be crucial in helping Leicester on their journey back to the top flight.
Maresca is set to ring the changes at the club, with Harry Winks, Zack Steffen, Conor Coady and Joel Piroe all linked with a move to the east midlands.