The 5,000 metre world champion and Arsenal fan told Shortlist that he did not run against the North London club's famously speedy winger when he recently met the team.
"I think we should do it for charity," he said of the prospect of a match-up. "What do you think? 200 metres?"
On learning from his agent that Walcott has run 100 metres in just 10.8 seconds, Farah added: "Seriously? Okay then, we'll do 400 metres."
Talking about meeting the Arsenal team, he continued: "I was lucky enough to be invited to watch them train, and Arsene Wenger asked if I'd like to run out with them on the training pitch, which was one of the best days of my life.
"I didn't take part in a physical game in case I got injured, but I passed the ball around a bit - my passing was awful."
London 2012 hopeful Farah came third in last year's BBC 'Sports Personality of the Year', behind winner Mark Cavendish and runner-up Darren Clarke.
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Watch Mo Farah in his recent 'make it count' advert for Nike below: