The soft-drinks giant believes the BLUE ORCHID rocker is the only musician with enough talent to write a track to rival the impact of I'D LIKE TO BUY THE WORLD A COKE - which became a huge hit after featuring in Coke's 1971 ad campaign.
An advertising source tells Britain's New Musical Express, "Coke have been talking to Jack about getting him to write a new song and he's very interested.
"They believe Jack is the only artist who can deliver them something that will be timeless."
However, the hitmaker - who refused to appear in a Gap commercial in 2001 - is still considering his options because he fears teaming up with the international corporation could upset his fanbase.
A band source says, "He's been asked to do it and is just deciding whether or not it's a good idea.
"The White Stripes turned down a Gap advert, so if they did it it'd probably be a case of Jack writing a new song for the commercial."