The Mirror understand the Toffees have placed the ex-Fleetwood Town forward at the top of their transfer wishlist ahead of the off-season after a meeting regarding their summer recruitment.
But the report adds that he would be tempted by the prospect of moving to Goodison Park, where he would rival Wayne Rooney - who earns £150,000-a-week - as the Merseysiders' highest earner.
Key to Everton's interest is director of football Steve Walsh - he left Leicester in July 2016 - having bought Vardy to the club for £1m in 2012.
After a lean 2016-17 campaign following Leicester's title-winning season, Vardy has returned to his best form this term to help Claude Puel's side occupy a top-half place.
In 32 appearances in all competitions Vardy has netted 15 goals while only Mohamed Salah, Harry Kane, Sergio Aguero and Raheem Sterling have netted more times in the Premier League.
The return to form is expected to see Vardy take his place in Gareth Southagate's England squad for the summer's World Cup finals when he will get another chance to enhance his reputation on the global stage.
As recently as the January transfer window Vardy was linked with a move to Manchester United, as Jose Mourinho looked to improve his forward line.
The Daily Telegraph first reported that United were keen on Vardy - they would later sign Alexis Sanchez from Arsenal - but having been quoted £75m to complete the signing they withdrew from the race, reported the Leicester Mercury.
Speaking following the reports of interest from United, Vardy admitted to being unaffected by the speculation and remains focused on his performances for Leicester.
"It doesn't affect me," he told Sky Sports. "You just take it with a pinch of salt, it's just rumours. Someone has started it off or someone has thrown a few pound on you at a local bookies, that is what gets it all starting.
"I am here at Leicester, concentrating on Leicester until Leicester tell me otherwise. Yes [I am staying], I'm here."