Wenger, 67, has been criticised by some fans after Arsenal slipped to sixth in the Premier League following four defeats in their past five games.
A 10-2 aggregate loss to Bayern Munich in the Champions League added to the pressure and Wenger says he will make a decision on his future "very soon".
"He's a great man in my opinion," said Iwobi, 20. "I'd like him to stay."
Wenger's contract expires at the end of the season but he has been offered a new two-year deal.
"He's always helped me and developed me as player," Iwobi told the BBC's World Football programme.
"I don't think it's fair the way everybody criticises him. It's very unfair considering what he's done.
"He's always achieved fourth place, been in the Champions League and been up there with the title contenders."
Contract negotiations with two of Arsenal's star names, Alexis Sanchez and Mesut Ozil, have been put on hold until the summer, and Iwobi hopes an agreement can be reached over their futures.
"As you can see from stats, goals and chances they create they are key players in our team," he said.
"Everything offensively almost goes through them. Even though we have other players they are world-class players.
"For the club it'd be great for them to stay, but at the end of the day it's their decisions."
Arsenal forward Alex Iwobi wants Arsene Wenger to remain as manager and says criticism of the Frenchman is "unfair".