A Daily Telegraph investigation says Allardyce used his role to negotiate a £400,000 deal and offer advice on how to "get around" rules on player transfers.
Allardyce is yet to respond to the allegations, and was due to meet with Football Association chairman Greg Clarke and chief executive Martin Glenn on Tuesday.
"You have to let Sam Allardyce defend himself and I just hope he will clear his name," said Wenger.
Karren Brady, chief executive of Allardyce's former club West Ham, said she is "both saddened and disappointed" by the developments.
"This is a man who spent his whole life trying to get that job, and got it in his 60s. What a great shame if he loses that job through non-footballing reasons," she told Radio 1 Newsbeat.