Walcott comes off contract in June.
Asked if the winger would be sold if the impasse continued into 2013, Wenger said simply: "No."
Pressed on whether Walcott would see out the season at Arsenal come what may, he replied: "Yes."
Asked if talks were closer to bearing fruit, he joked: "If I listen to you then every day it gets more expensive.
"We continue in a positive way. I told you many times we have until the end of December to sort this out."