The 63-year-old, who was the last manager to guide the Blues to silverware, said that the chance to secure a major trophy should take precedent over Champions League qualification.
"At the moment the top four takes second place," he told talkSPORT. "There's a great chance of a Wembley visit where they can lift some silverware and David Moyes can get the trophy on his CV he's craved for years.
"I'm sure the FA Cup will take priority."
The Toffees currently lie seven points away from a Champions League place in sixth, but set up an FA Cup quarter-final tie against Wigan Athletic with last night's 3-1 win over Oldham Athletic.
Royle lifted the FA Cup with Everton in 1995, with Paul Rideout scoring the only goal of the game in their Wembley final against Manchester United.