Walcott has been sidelined since he ruptured his knee ligament during Arsenal's 2-0 defeat to Tottenham in the third round of the FA Cup in January.
The injury cruelly ended Walcott's hopes of representing England at the FIFA World Cup in Brazil.
But in a boost ahead of the 2014-15 Premier League campaign, Wenger told Arsenal's official website that he was pleased with the 25-year-old's work thus far.
"He's progressing very well," Wenger said of Walcott, who scored five goals in 13 league appearances last season.
"He's worked very hard during the summer and we expect him to be back in full training at the end of August."
Wenger refused to put a timeframe on Walcott's return but said: "Once he's back in full training it can be very quick.
"He has a good basis, which is what he's working on now."
As winners of the FA Cup, Arsenal kick-off their competitive campaign against Premier League champions Manchester City in the Community Shield at Wembley on August 10.
Arsenal are in action six days later as they host Crystal Palace in their first Premier League fixture of the season.
