The Croatian has already fired five goals in seven games for the Toffees since his £5m January move from Rangers.
Royle, who became Everton's youngest ever goalscorer in 1966, said that Jelavic is showing "great promise" and could even reach the 20-goal mark next season.
"If you point Jelavic in the right direction then he'll score," Royle told the talkSPORT. "It's exactly what Everton have needed for a long time.
"Goals have been hard to come by for Everton and Jelavic is showing great promise. He could get near the 20 goal mark next season."
Royle has been without a job since departing Oldham Athletic in May 2009.