This despite him missing a spot-kick at Goodison Park last week with the scores level - Everton went on to win 2-0.
"Luka is our designated penalty taker. He scored so many penalties for us last season," said Hodgson.
"I have confidence that if we get a penalty on Sunday he'll score it."
He added: "We've got to keep working to make sure the chances are created and that we deny the opposition their chances to create.
"We have to do our level best to ensure that Arsenal don't make 12 [consecutive wins]."