Shore resigned from the Tottenham board over a difference of opinion with the Chairman.
Everton spokesman Ian Ross Said: "Bill Kenwright did have a meeting with Howard Shore, the two men are friends. But it took place last November and nothing has come of it. It was never going to be a takeover but simply a possible investment in the club. There are people talking to us about this sort of thing all the time."
Keith Wyness added: "There have been some preliminary talks. But we have talked to several parties and always have an open mind about such things.
"We obviously have a duty to look seriously at any offers that come along."