Walsh (left) with Leicester manager Claudio Ranieri
Walsh, who has gained a reputation as one of England's top talent spotters, is reportedly wanted as Toffees director of football. with talks said to have taken place this week.
Walsh with former boss Nigel Pearson, who brought him to Leicester in 2011
The report claims the former school teacher has not travelled with the Foxes to their Austrian training camp, nor has he been spotted at the club.
Walsh signed a new deal with the Premier League champions six weeks ago, meaning Everton would have to pay what is described as 'hefty' compensation to free him from his contract.
Everton's new investor Farhad Moshiri
The Toffees are looking to revamp their behind-the-scenes structure and previously failed with an approach for Sevilla director of football Monchi, the report claims.
Monchi's finds have helped the Andalusians to three consecutive Europa League titles, though Leicester utilised Walsh recruits Jamie Vardy, Riyad Mahrez and Ngolo Kante to bocame the unexpected champions of England last term.
Kante (left) is one of Walsh's best buys
Walsh's appointment could kick-start Everton's summer recruitment drive, with veteran goalkeeper Maarten Stekelenburg the billionaire-owned side's only signing so far.