Arzani joined the Scottish giants on a two-year loan deal from Manchester City following the FIFA World Cup and arrived with high expectations after dazzling defences in Russia.
But after Rodgers left the 19-year-old out of his 43-man UEFA Europa League squad last month, citing a lack of fitness, the skilful winger is yet to feature for the first team.
And Wallace, winner of five league titles and Celtic's lone European Cup, believes questions must be asked of Rodgers' reasoning.
"Arzani is a good little player, and Brendan Rodgers disappointed me on that one," Wallace said.
"He’s saying it’s going to be a while before he plays. Well, why are Celtic paying the wages and not Man City?
"If I was the board at Celtic, I’d have kicked the manager’s a*** out the door.
“Why would you take Arzani for two years if he isn’t going to play in your team? The kid, for me, will finish up a better player than James Forrest.
"Arzani is quick, he takes people on, and he reminds me a bit of Jimmy Johnstone because of that.
"He doesn’t have Jinky’s trickery, but he gets balls over, and did really well at Melbourne City for a couple of seasons.
"When I heard Rodgers say he wasn’t ready, I was baffled. Why take the boy if he thinks he’s not ready?
"If I was the lad, I’d ask to go back to [Manchester] City or go somewhere else to get a game."
The Hoops, aiming to clinch their eighth consecutive Scottish Premiership, have started the season well below their lofty standards and currently sit third, three points adrift of leaders Hearts through eight games.
Arzani meanwhile has been a standout figure in the reserve team and is currently away on international duty with the Socceroos.
