The former James Bond star reached out to Mark Gatiss online after the Sherlock co-creator praised the veteran actor for his "wonderful" performance in 1970 thriller The Man Who Haunted Himself.
Responding to the compliment, Moore cheekily tweeted, "I might be equally wonderful in Dr Who (sic) or Sherlock if asked!" - and it appears his brazen approach has paid off.
An excited Gatniss replied, "My life is complete! Will be (in) touch."
The screenwriter has yet to expand on the kind of role he has in mind for Moore for either Sherlock, starring Benedict Cumberbatch as the literary super sleuth, or Doctor Who, which features Matt Smith as the Time Lord.
If Moore appears in the futuristic sci-fi series, he won't be the only 007 agent to have joined the franchise - his Bond successor, Timothy Dalton, was cast in two Doctor Who episodes in 2009 and 2010 opposite former Time Lord, David Tennant.