The forward's current deal with the Gunners expires in the summer, and the player is now free to negotiate pre-contract terms with foreign clubs.
However, reports claim that the England international is close to agreeing to stay on at the Emirates Stadium, and Wenger hopes that the deal is close to completion.
"I hope that [a deal] is not far," Wenger told reporters.
"As long as he thinks I'm not done, it's not done but that's the first important work we have to do and hopefully we can do that very quickly."
Walcott was in the Arsenal side that beat Swansea City 1-0 in their FA Cup third-round replay on Wednesday night.