The newspaper paid Armstrong £300,000 to settle a libel case for suggesting that he may have cheated.
The USADA subsequently found that he had led the “most sophisticated” doping programme in sporting history.
The Sunday Times is reportedly demanding the return of the original settlement payment, along with interest and legal costs.
Mumbai Roundup: 9 incidents that took place this week
Photos: Ajay Devgn, Parineeti, Tabu at 'Golmaal Again' trailer launch
Photos: Dipika Pallikal Karthik oozes oomph in bikinis and sarees
Photos: Kareena Kapoor Khan's grand birthday bash
Photos: 'Dangal' girls Sanya Malhotra, Fatima Sana Shaikh's dinner outing