The England international, who joined Arsenal as a 16-year-old in 2006, signed a new three-and-a-half year deal in January 2013 after drawn-out negotiations.
However, with that contract set to enter its final 18 months manager Wenger is keen to tie Walcott to fresh terms.
"We are starting to sit down with him," the Frenchman told reporters.
"I think he has one-and-a-half years to go on his contract in December and it is never an easy job with him, you know."
Walcott returned to action following a 10-month absence with a cruciate knee ligament injury when he came off the bench in Arsenal's 3-0 Premier League victory over Burnley last Saturday.
Having established himself as pivotal figure in Arsenal's first-team, Wenger believes the 25-year-old winger is reaching the peak years of his career.
"Will he be at his peak in the next few years? He should be, yes," he added.
"He is 25. It is the best years now so hopefully we can profit from that."
