Producers plan to capitalise on the popularity of London 2012 and are targeting the most successful British gymnast of all time, as well as other Team GB stars.
Tweddle, a three-time world champion, will retire after the Games but she has yet to sign up to Strictly.
"The bosses have made it clear their priority is to secure as many London 2012 competitors as possible," a source told The Sun.
"The Games are by far the biggest event of the year and they want to reflect that by getting some big sporting names on board. The attitude is that if someone has won a gold medal, we should be considering them.
"But securing Beth would be a big coup. She is a popular member of the British team and her retirement leaves her able to consider other projects.
"There's no doubt she would be capable of some phenomenal moves on the dance floor. Nothing is confirmed yet but we have our fingers crossed."
Tweddle led Team GB's women's gymnastics squad to sixth place in the team event earlier this week - the highest position since 1928. She will compete in the final of the uneven bars on Monday (August 6).
Chris Evans and World Snooker Champion Ronnie O'Sullivan have been linked to Strictly Come Dancing. Dannii Minogue has denied reports that she will compete in the show.
Photo gallery: Rumoured celebrities for Strictly Come Dancing 2012:
Copyright: PA Images Dominic Lipinski/PA Wire