The agency is believed to be working on a TV campaign for "Modern Essentials Selected by David Beckham" that will break in October. It was filmed in New York.
Teaser pictures have begun to appear on the social media accounts of Beckham and the US comedian Kevin Hart. The images show the pair wearing matching outfits and striking similar poses.
In one shot, the pair are in white trousers and orange tops, passing a leather medicine ball to each other.
An H&M spokeswoman said: "We do not comment on rumours." Adam & Eve/DDB would not comment on the appointment.