Farah, who won gold at the 5,000 and 10,000 meters at the London Olympics last year was the star turn of the Games along with Jamaican sprinter Bolt, who won the 100 and 200 meters.
"It would be great to do a distance where people vote in - proper athletics fans - on what distance they think is most suitable," Farah told Sky Sports.
He then turned to the camera and said: "Are you up for that? Come on, you've got to do it."
In a separate interview, Bolt was shown the footage and replied he would be prepared to take on the challenge.
"That sounds fun," he said.
"It's going to be hard but it's charity so it's all about fun and enjoyment.
"I'm up for anything, for anything's possible."
Bolt, who holds the world records at 100m and 200m, said running 1,500m would be out of the question.
"It's way too far," he said. "600 for sure I can try because I've done 600 meters in training, but not 1,500 meters."
Farah, the Somalia-born 30-year-old who grew up in London, has lightning pace over the final stretch and has recently experimented with shorter distances, setting a European 1500m record of 3:28.81 this summer.
Farah laid down the challenge to the Jamaican sprinter after running a personal best of 7 minutes 36.
One intriguing aspect of the race would be how the taller, more powerful Bolt would cope with the early stages of the longer distance and if he would have the acceleration to match Farah's finish after running 500 meters.