First off, this is not a 100% definite thing. I just read something about this recently and wanted to ask. I still think it's more likely he's INTJ, but there are some interesting thoughts on an INTP type. I originally thought the detective L from Death Note was an INTJ, but after listening to peoples arguments, I could see where the INTP idea comes from, and I thought that Holmes also shared some of this sort of trait. He has a vast array of knowledge on the subject of his proffesion, and is often very organised in some ways, which is J like, but in other ways, such as the condition of his home, he is very disorganised and messy, which is rather more P.
Firstly, his motives for detecting. These aren't always entirely clear, I don't think. Sometimes he shows a lot of interest in the traditional justice and purposeful stance of an INTJ, and he did shoot V.R (Victoria Regina) into his wall, which was pretty patriotic one would think. However, it is repeatedly stated that he only takes on cases thatchallenge his mind and that really interest him, which seems rather INTP in the search for knowledge and intellectualism without a whole lot of concern for tha final outcome (keeping the country safe and fighting for a purpose). In fact, I think he sometimes complains when there is no criminal activity because he loves his job so much.
One of the things I think is a misconception about Holmes is the idea that he is ISTP. Apparently, because he has so much motivation and determination, notices details, enjoys the occasional fistfight and is capable of doing footwork, he is not an INTP because all INTPs are inconquerably lazy and only 100% interested in purely intellectual matters and oblivious to reality. Needless to say, I think this is rubbish. I understand the claim that an ISTP can think intuitively and make connections between situations using Ti and you don't have to be an N to do this sort of thing, but at the same, Sherlock Holmes' focus so overwhelmingly intellectual. He has made his sole purpose in life the discovery of facts and information, a lot of the time requiring him to imagine potential possibilities before the evidence has even arrived and then 'eliminate the impossible' until remains the truth. I have seen plenty of S detectives in TV shows but I cannot imagine an S denying themselves almost entirely of earthly pleasures such as sleep, love (debateable/he might be entirely asexual and aromantic) and such just to think. Holmes spends many hours on end silently thinking about a case while Watson goes about his life. In the Dancing Men, he absolutely jumped for joy at the thought of studying and solving a complex cryptogram and put many hours into it. And as much as an S can think intuitively, so can an N notice fine details. It's not your ability but your preference that defines your type. He also likes the occasional fight. So do I (well if I COULD fight, I would, plus I used to do fencing and enjoy it) and I'm definitely an N. He gave up boxing to detect anyway, so you can see his preference lies in that section. And INTPs I have known, including myself, are willing to put a lot of work into something if we find it really interesting, so footwork is hardly an anti N excuse.
Anyway, other opinions are welcome. Love to hear what you think on the subject. Please correct me if I have made any blatant logical errors.