The Gunners boss has had a new bid for long-term target Phil Jagielka of Everton turned down this week, whilst he maintains an interest in Bolton's Gary Cahill and Blackburn's Chris Samba.
And he admits he is still battling to bring in a new stopper before the start of the new season.
"Certainly, we will have to find one more defender," said Wenger.
"I can promise we will work very hard on it. It will all speed up in August.
"In fairness, everybody looks for players. Everybody looks for the same area and you see that nobody turns up with magic. It's all about being steady, working very hard on it and being calm as well."
Wenger refused to comment on any of his defensive targets like Jagielka and Cahill, saying: "I don't want to comment individually because I do not want to destabilise clubs.
"I do not want to do to clubs what some clubs do to us, so I wouldn't like to comment individually on any player."