The Gunners made an improved 40 million-pound bid for the Uruguay international earlier this week, but with Anfield managing director Ian Ayre confirming the bid was rejected, Arsenal remains a long way away from agreeing a deal.
"We are ready to do quick deals but all the transfers do not depend only on us. We are prepared to wait.
"There is nothing to say [on the Suarez deal]. I have been away now for two or [three] weeks and it’s hard to see how things are advanced because everyone is on tour at the moment and it’s very difficult to get in touch with people.
"It looks very unlikely that we will have anyone before the Emirates Cup next week, but we still have a strong squad."
Although Arsenal has only made one signing this summer, Yaya Sanogo on a free transfer from Auxerre, Wenger is confident his current squad has what it takes to win silverware this season.
"With or without additions we can be title challengers next season," the French boss added.
"What we want is not a name but a good player. The name is less important. What is more important is the quality of the player. At the moment I must tell you we are not close to signing anybody.
"Of course we want to do as many top players as we can, but we also have to focus on the players we have and develop them."