The 23-year-old will be out of contract in the summer but has been in excellent goalscoring form for the Gunners recently.
Wenger has spoken repeatedly of his intention to keep the England forward at the Emirates Stadium, and the Arsenal boss said at a press conference this morning: "We are talking."
He added: "It is very difficult to be predictable in these kinds of situations but our desire is there to do it as quickly as possible and ready to do it."
Walcott has scored 14 goals across all competitions for Arsenal so far this season, already his best total in a single campaign since moving to the north London club from Southampton in 2006. He is keen to operate as a central striker and proved his worth in that position with a hat-trick in the 7-3 victory over Newcastle at the Emirates last Saturday.
"He definitely has all the attributes to play up front," said team-mate Alex Oxlade-Chamberlain of Walcott following the Newcastle win.
"The goals are coming. He has proven he can do a really good job for us up there.
"For someone with his pace it's hard for anyone to defend against and when he gets the service he can always punish teams so he's doing really well."
The Arsenal fans who spent a large portion of the last 18 months questioning Walcott's ability were instead urging Wenger to "sign him up" on Saturday as the player saluted all four corners of the ground on an impromptu lap of honour.
Walcott turned down a new contract - reported to be worth £75,000 a week - in the summer and has failed to reach an agreement with the club ever since. The club have reached agreement over new long-term deals with a number of their other young stars, including Kieran Gibbs, Jack Wilshere, Aaron Ramsey, Oxlade-Chamberlain and Carl Jenkinson.