The England international has been mooted for departure from the Emirates this summer, with Liverpool previously linked to the 23-year-old.
"Negotiations are ongoing with Walcott and we want to try and sort it out one way or the other before the transfer window shuts," said Wenger.
"Both parties are still around the table, so it would not be right to deal in what happens if we do not reach an agreement. We want him to stay, and hopefully that is the outcome."
Walcott has just one year remaining on his current deal.