The England forward's current deal runs out in the summer, and the club have been in negotiations to close out terms on a lucrative extension which would make Walcott among the highest-paid players at the club with a five-year contract worth around £90,000-a-week, boosted by lucrative add-ons.
While not taking anything for granted, Wenger hopes a positive end to the saga can be reached in the coming weeks.
"We are on a good road but in this situation as long as nothing is signed, you are cautious, but I am optimistic we will get to a happy conclusion," said Wenger at this morning's press conference ahead of Sunday's Barclays Premier League clash against Manchester City.
"I was optimistic last week, but I am a bit more optimistic this week.
"Discussions progress smoothly, but slowly."