The James Bond veteran responded to a tweet from Sherlock co-creator Mark Gatiss praising his "wonderful" performance in 1970 film thriller The Man Who Haunted Himself.
@markgatiss thank you. I might be equally wonderful in Dr Who or Sherlock if asked!— Sir Roger Moore(@sirrogermoore) May 26, 2013
Gatiss then replied: "My life is complete! Will be [in] touch."
Timothy Dalton - Moore's successor in the role of James Bond - previously starred in Doctor Who in 2009/2010, appearing opposite David Tennant in two-parter 'The End of Time'.
Doctor Who will return to BBC One for its 50th anniversary special in November, while shooting on the third series of Sherlock will resume in late summer.
> Sherlock September return date rumours denied by cast, crew
Watch a clip from Doctor Who below: