Arzani's two-year loan deal from Manchester City with the Hoops is set to expire whenever this season concludes.
Wilson, head coach of Brechin in Scotland's second tier, has appealed to his former club to re-sign the 21-year-old attacker.
"There's a part of me that thinks he deserves to be given a chance," said Wilson to the Scottish Sun.
"He has been unlucky with some serious injuries.
"Celtic always seem to attract good wingers but I just think the fans would like to see a bit more of Arzani before he gets shunted back to his club."
"I think another loan deal would be the best way."
Arzani is currently back on Australian soil having been granted leave by Celtic during the COVID-19 crisis.
His time with the Bhoys has been cruelled by a torn anterior cruciate ligament, and since his recent return from the injury he has been unable to break into coach Neil Lennon's plans.
The World Game reported last month that Arzani's management team have begun talks with parent club City over a new destination - with clubs in Germany, the Netherlands and Belgium being looked at.
