The Gunners have been heavily linked with both creative influences during the summer transfer window.
Arsene Wenger already has plenty of similar options at his disposal, but uncertainty continues to shroud the future of star forward Alexis Sanchez.
If an addition is to be made in that department before the deadline passes, then Arsenal have been urged to turn their attention in the direction of the King Power Stadium, rather than Goodison Park.
Former Gunners striker Smith told talkSPORT: “I’d say [Arsenal should go after] Mahrez more than Barkley.
“I think he’s more of a match winner and he’s a more mature player.
“I’ve just come back from Hong Kong watching Liverpool and Leicester in the Asia Trophy, and Mahrez looked sharp.
“Whether he’s playing for a move, putting himself in the shop window, I don’t know.
“He’s definitely a Champions League player, although I know Arsenal aren’t in that competition this season!”
Mahrez is said to have registered on Arsenal’s radar for some time.
He made Leicester aware of his desire to move on in May, having honoured his promise to spend one more season with the club on the back of their remarkable Premier League title triumph.
There have, however, been no suitable bids lodged for his services as yet and he remains with the Foxes.
Barkley, meanwhile, has also made it clear that he wants to take on a new challenge, having opted against penning fresh terms at Everton.
Ronald Koeman is expecting the England international to move on but he too is waiting to discover which club, if any, will make a formal approach.