The Gunners boss refused to rule out a bid for Sevilla striker Carlos Bacca but insisted he could not make any guarantees about new players.
Goal understands the Gunners are poised to make a bid for the Sevilla striker, with Olivier Giroud ruled out for up to four months with an ankle injury.
Yaya Sanogo started up front as Arsenal was held by newly promoted Leicester and following the game, Wenger did not deny his interest in the Colombian.
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When quizzed regarding a move for Bacca, Wenger replied: "I can give you my phone and in the next 24 hours you will see you get plenty of people offered from all over the world. We can talk and talk and talk. At the end of the day we sign somebody or not.
"Could we win the game today without anybody? Yes. We have plenty of strikers and even when we had Giroud - now everybody says we cannot replace Giroud - when you had Giroud you asked me the same question.
"It's a recurrence as long as the transfer market is open to make everybody dream by thinking the solution is always somewhere, when it's not necessarily obvious."
Wenger confirmed the club is open to signing new players ahead of the transfer deadline on Monday night.
"We are very active," he told reporters. "The solution every time you don't win a game is to sign somebody anyway. We are out there and we try our best and you have to trust us to find the best possible solution, but as well not to think every time you don't win a game that there is a miracle man who wins you a game.
"I don't want to promise what I am not sure of. I have worked long enough in England to know that I don't like to promise what 100 percent doesn't depend on me."