The 29-year-old started all 38 of the Foxes’ Premier League fixtures last season as Claudio Ranieri’s boys unexpectedly claimed the English title, recording 80 saves and 15 clean sheets.
However, Leicester have already suggested they’d be willing to part with the Danish international this summer by signing a potential successor in one-time Manchester United youngster Ron-Robert Zieler.
And Everton believe they could tempt Schmeichel away from the King Power Stadium by offering to double his current £35k per-week wages.
Likewise, the 6 foot 2 shot-stopper is well within the Merseyside outfit’s financial reach due to a £17million release clause – also meaning Everton won’t have to barter over price-tag with the Foxes.
The Liverpool Echo claim Ajax No.1 Jasper Cillessen is also on the Toffees’ list of potential successors to Tim Howard, who has joined MLS side Colorado Rapids.