The Gunners decided to extend Luiz's contract until 2021/22, much to the chagrin of many supporters after the Brazilian's recent errors.
And Parlour thinks Arteta could use the 33-year-old higher up the ground to avoid more mistakes.
He told PA Sport: "He makes too many mistakes, and at 33 he is not going to learn.
"You have to look a little bit higher than David Luiz.
"He could be a squad player and you could play him as a holding midfielder.
"He has got a range of passing and you know if you make a mistake there you have centre-halves behind you, that could be a role for him."