Walcott, 23, is out of contract at the end of June and is free to start discussions with foreign clubs from next month.
A clutch of Premier League rivals, including Chelsea and Liverpool, are also thought to be interested in the England international.
Wenger had previously stated his desire to finalise Walcott's contract before Christmas. However, that scenario looks increasingly unlikely, with the Frenchman revealing the winger has yet to make up his mind.
He said: "We have not made any progress but I am honestly frustrated about it. It is clear with the player and he knows what I want. He has to make up his mind.
"We have been in negotiations for a long time and we have not been late in our re-negotiations with him and we always try to extend contracts very early."
But Wenger is confident Bacary Sagna will sign a new contract and has rubbished reports the full-back has been left dismayed by the terms on offer.
"I do not understand these speculations," he said, ahead of Saturday's clash against West Brom at the Emirates.
"He has one-and-a-half year of his contract to go, and we are in negotiations with him to extend the contract which are very positive, so I am quite amazed by these statements because it is completely opposite of the feelings we have with the player, and with the negotiations we have about his extension."