The Gunners made an improved £40 million bid for the Uruguay international earlier this week, who is willing to submit a transfer request in order to force a move.
But, with Anfield managing director Ian Ayre confirming that both bids thus far were rejected, Arsenal remain a long way away from agreeing a deal, but Wenger is prepared to bide his time.
|10/1||Arsenal are 10/1 with BetVictor to win the Premier League
"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 have only made one signing this summer, Yaya Sanogo on a free transfer from Auxerre, Wenger is confident his current squad have what it takes to win silverware this season.
"With or without additions we can be title challengers next season," the French boss added.
"We try to do the job and we will try to do it well, but nothing has been concluded with anybody.
"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."