Walcott’s situation has dominated the headlines in north London for months, with the 23-year-old’s current Gunners deal set to expire in the summer.
It is understood that the England international agreed a new deal worth around £90,000-a-week in recent days but is yet to sign.
And Wenger on Friday hinted that Walcott is closer than ever to committing his future to the north Londoners.
“We are on a good road but in this situation as long as nothing is signed, you are cautious,” he said. “Discussions are progressing slowly, but smoothly.
“I am optimistic we will get to a happy conclusion. I was optimistic last week but I’m a bit more optimistic this week.”
Asked if Walcott will sign before the end of the month, Wenger said: “Yes.”
Walcott has been in impressive form for Arsenal this season, scoring 14 goals in all competitions and providing 10 assists for his team-mates.
Arsenal take on Premier League champions Manchester City at Emirates Stadium on Sunday afternoon.
Asked about potential new arrivals at Arsenal this month, Wenger added: “We still work on the transfer market, but do not want to bring in average [players].”
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