Walcott missed last week's Champions League 2-0 victory over Montpellier and Saturday's scoreless draw with Aston Villa after injuring his shoulder in the 5-2 win over Tottenham Hotspur in the north London derby 10 days ago.
Wenger confirmed Tomas Rosicky was back in training after a long layoff with an Achilles injury picked up while playing for the Czech Republic at Euro 2012.
The manager said he was not worried that England's Jack Wilshere, himself recently returned from a 14-month spell out with an ankle injury, would follow Robin van Persie, Samir Nasri and Cesc Fabregas out of the Emirates Stadium.
Wilshere has more than two years left on his contract but the club are keen to nail him down long-term.
"Jack has always been very committed to this club and I hope he will show that," Wenger told a news conference.
"There is only one way to show that and that is to commit your long-term future to the club."
The 20-year-old was kept on the bench against Aston Villa but Wenger said he was likely to play against Everton.
- Sports & Recreation
- Aston Villa
- Jack Wilshere
- Tottenham Hotspur
- Tomas Rosicky