The Wimbledon tennis champion and his girlfriend are allegedly being lined up by chief creative officer Christopher Bailey to star in the British brand's next couples-themed ad campaign.
A source told the Daily Mail newspaper: ''Andy may not seem like the obvious choice for a fashion campaign, but he has proven he can scrub up incredibly well.
''He is in great shape and has that great bone structure which Burberry loves. Kim is gorgeous and has amazing hair.''
Rumours first emerged when the pair arrived at the Wimbledon Champions Dinner last week clad entirely in Burberry, with Kim donning a £3,500 Burberry Prorsum gown.
It has been reported that Scottish sportsman Andy's manager, Simon Fuller - who also looks after the Beckham family - is orchestrating the deal after successfully landing 10 year old Romeo Beckham his first modelling job.
Andy, 26, and Kim, 25 - who have been dating for seven years - could follow in the footsteps of new Burberry muses, Sienna Miller and her husband Tom Sturridge, whose racy new campaign was unveiled earlier this month.
A Burberry representative said: ''We never comment on campaigns until they are announced.''