The Gunners’ new interim boss takes charge of his first game in the hot seat against Norwich on Sunday, after replacing sacked Unai Emery.
Luiz was a regular performer under Emery having been signed by the Spaniard in the summer, but has failed to help solve Arsenal’s defensive issues.
“Whoever they decide to bring in after Freddie Ljungberg will be inheriting the same problems that Emery failed to fix,” Keown told the Mail.
“Their lack of solidity at the back, for example. For Norwich on Sunday, I’d have David Luiz on the bench.
“Sokratis and Calum Chambers would be my centre backs and I’d have Lucas Torreira deep in that midfield, patrolling that area in front of them.
“Get that triangle right, then build the team from there. Whoever comes in after Emery’s exit, he has a big job to do. The board have to get this one right.”
The transfer of Luiz was seen as a shrewd move by Emery after landing the experienced centre-half from rivals Chelsea for £8 million.
But Keown would like to see his former club move for Man Utd’s Chris Smalling , who is currently out on loan at Roma.
“Smalling is doing exceptionally well – £13 million, the price they are putting on his head, that’s not enough,” Keown said on BT Sport.
“Arsenal could maybe do worse than to take him.”
Arsenal moved to sack Emery following the club’s worst run in over two decades.
In an official statement announcing his dismissal, the club blamed “results and performances not being at the level required”.
They added: “We have full confidence in Freddie to take us forward. The search for a new head coach is underway and we will make a further announcement when that process is complete.”
It is believed Ljungberg will be given a chance to stake his claim for the role on a permanent basis, but does not top the list of potential candidates drawn up by the Gunners board,
Leicester manager Brendan Rodgers is first choice, but would cost Arsenal £14 million in compensation were he to make the switch to the Emirates.
Former Arsenal captains Mikel Arteta and Patrick Vieira are also among those linked.