With Kevin Mirallas having returned from a long-term hamstring problem and Victor Anichebe pressing for a recall to the starting line-up, Jelavic could be rested to the bench for Saturday’s FA Cup fourth round tie at npower Championship side Bolton Wanderers.
And Distin has laughed off any suggestion of going easy on the Croatian during training at Finch Farm to help bolster the striker’s confidence.
“I’m trying to help him out in training, but then I have to make a choice... is it him or me?” added Distin. “And I have to think about myself! It’s not like he is 18-years-old and I’m going to let him score a few. That wouldn’t do him any good.
“When he’s out on the field during a match, the opposing defenders aren’t going to let him score. They’ll be defending hard against him.
“We have to do that in training and I’m sure we’ll soon see his confidence coming back.”
Everton have withheld permission for on-loan Ross Barkley to appear for Leeds United in their FA Cup fourth round tie against Tottenham Hotspur this weekend.
Goodison manager Moyes is unwilling to see Barkley cup-tied ahead of his scheduled return to Merseyside next month.
Leeds manager Neil Warnock said: “We're looking into whether he could play if Everton lose.”
Meanwhile, Everton are waiting on tests on Seamus Coleman with fears growing the Republic of Ireland defender is facing another spell on the sidelines.
Coleman hobbled off during the second half at St Mary’s after injuring his thigh while blocked a cross from Southampton’s Luke Shaw.