The 55-year-old, who played for both clubs and is a boyhood fan of his hometown club Leicester, told the Everton site's official radio show that there is no need for Toffees fans to panic about their underwhelming season.
The player-turned-TV host, who scored 40 goals during his only season at Goodison Park after leaving the Foxes in 1985, is confident that Roberto Martinez's side can compete right at the top of the Premier League if given a little more time to gel.
He told evertonfc.com: "It has been a bit hit and miss in terms of results [this season] but Everton are one of the sides that I really love to watch. They play great football and the entertainment value, for me, is a big part of the game.
"They have been unfortunate in some games and perhaps let things slip when they shouldn’t have done - but I wouldn’t be panicking as an Everton fan with the players the club has.
"They have resisted other clubs trying to get those players, which is a good sign, and they have got the makings of a side who could go on and do something like Leicester have done. That’s not beyond the realms of possibility next season if they can keep the current bunch together."
The Toffees have endured an underwhelming season so far after finishing outside the top half for the first time in a decade last campaign, and they currently sit in 11th place in the league table.
However, they are just six points off a guaranteed Europa League spot with 12 games still to play, and in key players such as Romelu Lukaku and Ross Barkley, who have scored 33 goals in all competitions between them this season, they have some of the brightest young talent in the top flight.
The Merseyside club next play again on 1 March, when they travel to bottom side Aston Villa.