The Welsh midfielder has gone from being a figure of complaint to a fans' favorite thanks to his sterling 2013-14 form and the Gunners manager feels that he can improve further.
Once a highly criticized figure by Gunners supporters, the Welshman has been in imperious form in 2013-14 and his boss admits that he was considering dropping the midfielder to spare him the crowd’s frustrations.
"Let's not forget that, one year ago, people were saying to me: 'It's difficult to play him at the Emirates [Stadium],'" Wenger told the press. "You could see there was an impatience with him at home. You always are, as a manager, in a period where you think: 'Do I push him through and he can go more down or do you give him a breather - to regenerate, to get him a fresh start?'
"That's always difficult for us to assess because it is linked to their mental state. When their own confidence is down, of course, they are in trouble but he is a confident boy. You have to give Aaron credit for that transformation - the credit goes to him because he could deal with that. He has shown he could come back, never give up, convince everybody that he has the needed quality."
Ramsey's progress was set back for a long time by a broken leg suffered in a challenge with Ryan Shawcross in February 2010 but Wenger feels that he has recovered and is now on his way to fulfilling his vast potential.
Asked if the midfielder is a world-class player, the Frenchman replied: "He can become [so]. I think always you know what you want, I do not judge people when I look back at their career [on whether] they were world class or not world class.
"I always think: 'Has this guy done the maximum with the potential he had?' And the respect I have for a guy is how far he has gone towards his potential. Of course, when you play at Arsenal you need already to be a world-class player, because you go through so many selections - you need to have some special talent. What is for me most important is has a player gone as far as he could?
"He's 22 years old. I'm 64 and I still think I can improve, so why should a guy who is 22, who can play until he is 35, think he is the top of his game? It's impossible. If he has the right attitude, he will continue to improve."