The north Londoners have already brought in Alexis Sanchez, Mathieu Debuchy and Calum Chambers but Wenger has not ruled out strengthening his squad further ahead of the new campaign.
Speculation on Southampton midfielder Morgan Schneiderlin continues amid interest from both Arsenal and Tottenham - with the latter favourites, despite Ronald Koeman's insistence he will not be leaving the club.
However, as revealed by Goal, Manchester United's interest in defender Thomas Vermaelen also remains and that may see Wenger sanction a deal for a replacement before the season starts.
|6/1||Arsenal are 6/1 with Bet365 to win the Premier League this season|
Asked whether he was on the verge of any signings, the Gunners boss said: "No, not really. If a good opportunity comes up we might still do but at the moment we're not close to signing anybody.
"I'm very happy with the squad I have available at the moment but we might be short at the back, maybe."
Two of Wenger's arrivals made appearances for their new clubs during their 5-1 demolition of Benfica in the Emirates Cup on Saturday, and the 64-year-old was delighted with the crowd's reaction to Alexis Sanchez.
"Of course, a new signing will always get a big welcome, the crowd like that," he said of his second-half arrival. "You could see that he will be dangerous. He's not fit yet but once he is fit he'll be a dangerous player."
But he also reserved praise for strikers Joel Campbell and Yaya Sanogo, the latter hitting a first-half hat-trick and ending the match with four of his side's five goals on the day.
"He scored four goals," he said. "We could see it [scoring] was on his mind for a while and not only did he score one, he scored four. It's good for him that he can find that confidence because he has a great goalscoring record.
"It was a very good performance [from Joel Campbell]. He can go past people, he's creative in the final third and I like how he did today."