The Scot, who played alongside the Croatian striker at Rangers, believes the 27-year-old is showing more confidence in front of goal after netting three times in pre-season
The Croatia international striker marked his arrival following his January 2012 switch from Rangers with nine Premier League goals in 13 appearances, including two in a 4-4 draw with Manchester United at Old Trafford.
|125/1||Nikica Jelavic is 125/1 with bet365 to be the Premier League's top scorer
The 27-year-old has scored three goals in pre-season, one of which was a consolation strike in Everton’s 2-1 defeat against Real Madrid on Saturday, and Naismith is backing the forward to get back to his prolific best in the Premier League.
"Throughout pre-season he has looked sharp and he has got a bit of confidence back," Naismith told the club’s official website.
"I think last season he lost a bit of that through not playing every week.
"In training he has looked very sharp as well and maybe the signings that came in have put a bit of pressure on him and he wants to be starting for Everton."
Jelavic heads into the new season looking for only his second Premier League goal of 2013 following a barren spell in front of goal.