The Gunners have been linked with moves for both Mahrez and Barkley this summer but are not aggressively pursuing the talented duo, who are eager to leave their current clubs for a new challenge.
Smith, who played for Arsenal for almost a decade, thinks his former club need Mahrez more than Barkley as he believes the Leicester winger possesses the ability to decide games on his own, a trait that Barkley has rarely, if ever, shown during his Everton career.
"I'd say [Arsenal should go after] Mahrez more than Barkley," Smith told talkSPORT. "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!"
Tottenham's interest in Barkley has been well-publicised in recent months, but Everton manager Ronald Koeman said on Wednesday (26 July) that the Blues have yet to receive an offer from any club for the 23-year-old playmaker.
Everton saw fit to place a £50m price tag on Barkley earlier this year, but Tottenham are understandably reluctant to pay such a fee for a player in the last 12 months of his contract and are waiting for the Merseysiders' stance to soften before attempting to strike a deal worth around £25m.
Arsenal boss Arsene Wenger revealed his interest in Leicester's Mahrez last month and is believed to be considering a move for the Algeria international, who was also believed to be on Tottenham's radar. But the Gunners may face competition from Serie A outfit Roma, who are able to dangle the carrot of Champions League football.
Roma had a €23m (£20.6m, $26.8m) bid rejected by the former Premier League champions, who are seeking a fee closer to €40m, but the Leicester Mercury report that the Giallorossi are set to return with another offer of around €35m in the coming days.
The Foxes are keen for the speculation surrounding Mahrez to end and have made it clear that they want his future to be resolved either way before the first weekend of the Premier League season.