Vardy is one of Walsh's success stories at Leicester when he was head of recruitment at the King Power Stadium, overseeing the signing of the England international from non-league Fleetwood Town for £1m.
Now he wants to sign the forward once again for the Toffees, but his own position at Goodison Park is precarious with the club's transfer policy over the past 18 months being greatly criticised.
Walsh made the switch to Merseyside from the Foxes in the summer of 2016 and since then more than £200m has been spent on new players and PSV Eindhoven sporting director Marcel Brands is being lined up as a replacement.
Should the deal still go ahead?
Despite Walsh's links with Vardy should his presence at the club dictate whether a move is made for the forward - especially when looking at the 31-year-old's impressive statistics?
The Englishman's age may be something of a concern, but 16 goals in 33 matches in all competitions this season and 56 in 134 Premier League outings cannot be ignored and could be just what an Everton team struggling to find a solution upfront need.