Arsenal were linked with Sterling before he joined Manchester City instead but Harris, who says Wenger has the money to buy any player in the world other than Lionel Messi or Cristiano Ronaldo, is glad the Gunners steered clear.
“Sterling is a very, very good player but I’m very pleased Arsenal didn’t sign him,” Harris told the Daily Mail.
“He’s got a lot to learn. They were looking at him and the way he treated Liverpool wasn’t good. Arsene does a lot of work on the players before they get to us and he doesn’t take any nonsense.”
Wenger has two years remaining on his contract at Emirates Stadium and will be 67 by the time it expires, but Harris sees no reason why the Frenchman would not extend his deal.
“I’m sure we will want him to stay because he’s a good manager and the players respect him,” Harris said.
“Two or three years ago, when the crowd came after him, you could tell he was concerned, but I wouldn’t say he came close to leaving.
“He’s exactly the same as you see in the media – bright, determined and very conscientious about his players. He’s so fit and motivated that we hope he stays longer.”
Harris says Arsenal will have to break their club record to sign one of Wenger’s targets this summer but acknowledges it is not the Frenchman’s way to make too many changes to his squad.
“Tottenham sold a player for £80m, spent £110m and ended up worse off,” Harris added. “Arsene doesn’t think you should bring in more than three first-team players in one season because it takes too long for them to link up.
“He knows how to produce good players, too. We’ve got four or five very good youngsters coming through.
“With a bit of luck with injuries, I think we can challenge strongly for the Premier League and Champions League.”