With the last two "Sherlock Holmes" movies starring Robert Downey Jr. doing better business than expected and helping build interest in the film franchise, there have been rumors that the third movie is in the works.
The last concrete news about "Sherlock Holmes 3" was during 2015, and since that time, the movie has not been green lit. During that time, there was talk that the script was being crafted for the third movie, but since then, official news about the movie has been scant. IGN also quoted the producer of the film series Lionel Wigram stating that a script was being worked on. Right now, this could mean the script is possibly finished and more details pertaining to it could be released soon.
Importantly, the two "Sherlock Holmes" movies that Robert Downey Jr. has been part of were directed by Guy Ritchie and they managed to reboot the franchise successfully and make it more interesting. There has been a lot of interest in series and films around Sherlock Holmes recently; in fact, the TV series "Sherlock," which stars Benedict Cumberbatch as Sherlock Holmes and Martin Freeman as Doctor John Watson, has also been doing very well, but as with the film franchise, most of the interest is focused on the two central characters.
Therefore, if the "Sherlock Holmes 3" is announced, it will have to include Robert Downey Jr. playing Sherlock Holmes and Jude Law once again stepping into the shoes of John Watson. Right now, however, there are no indications that Robert Downey Jr. has enough time to devote to a third "Sherlock Holmes" movie as he is tied down with the superhero flicks in the Marvel franchise.
Meanwhile, the news that the script for the movie is being developed is welcome and there are indications that it could be based on one of the original stories penned by Sir Arthur Conan Doyle who created the books. Law and Downey Jr. have expressed interest in working on the third film so it is likely that if and when it is announced, both these actors will be on board.