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.
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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."