The 28-year-old is into the final year of his contract at the Emirates Stadium, and with there being no sign of him penning a new one, reports have claimed he could run it down and leave on a free transfer.
Manchester United are said to be among the clubs watching developments and could pounce if Ozil fails to agree fresh terms, but Wenger is hoping he stays where he is.
The Frenchman has admitted that contract talks have slowed down somewhat, but says they will pick up again with a view to securing the player's future.
"Yes, of course [I am hopeful]," Wenger said ahead of tonight's Europa League clash against Cologne. "The contract talks have slowed down a little bit since August 31, because we need a little breather and to focus on the competition. But we will slowly get back into that."