Trailing rivals Chelsea by 12 points, Arsenal’s wait for a first Premier League title since 2004 appears set to continue.
Much of the talk has surrounded Wenger, who has been at the club since 1996 but faces an uncertain future with his contract expiring at the end of the season.
Henry, a winner of two league titles with the club, feels there is no reason his fellow Frenchman should not extend his stay, although he has difficult problems to fix after a 3-1 loss at Stamford Bridge last time out.
“Personally, I don’t think Arsene has to go,” he told RMC.
“Does he have to change his tactics or his way of doing things? I don’t know if he’s willing to do that.
“But the work he has to do at the moment is difficult because it is mental work. What I saw against Chelsea is a mental problem. And it’s not easy to manage.
“For now, something is missing.”
Chelsea are runaway leaders in England, having won 19 of their 24 league games this season.
While Henry wants Wenger to stay on, the France World Cup winner said Arsenal’s squad appeared as strong as Chelsea’s ahead of the campaign.
“I think there is quality in this team, but is there enough to win the championship?” he said.
“At the beginning of the season, when you look at Chelsea and Arsenal on paper, there is not a huge difference. That means it’s possible.
“If Chelsea are ahead, Arsenal too can do it. But for that, you have to be in tune every day, you have to be good at training all the time.”
Henry added: “I think Arsenal players are not aware of what they can achieve. At some point, you have to believe in your chances of winning. It takes self-management and self-discipline in the group.”