The 25-year-old has been sidelined since January 4 and will miss England’s World Cup campaign in Brazil this summer.
"I'm not pushing myself to be fit for the World Cup or anything like that," Walcott told Arsenal’s official matchday program. "I want to be back quickly of course, but safely too.
"I want to try and be back for the early part of next season. That's the goal so there will be a lot of hard work throughout the summer and during the World Cup."
Walcott is buoyed by his progress after undergoing surgery in Janaury and is aiming to start running within the next month.
"It's nearly been four months now and my recovery has gone on track so far. At the moment, I'm working on muscle strength and building muscle in my quad. I've got a lot of the flexion back and I'm always working on extension,” he added. "A lot of the days are very similar, but the four months have gone really quickly. I don't see any point in being down in the dumps about the injury because it’s already happened and there are a lot of people with worse problems in the world.
"I'll just get on with my work - I'm first in and last out on most days. I see the consultant soon too and hopefully he'll give me the thumbs-up to push on even more. I'd love to be running in a few weeks."