This is one thing I have said in comments in other threads but I think it deserves a thread in itself to comment on, even if we can only speculate. I have searched and I see that it is usually claimed him to have lost them as most likely.
In a quora thread the voted as best answer is:
Statistically speaking, Satoshi Nakamoto is (in order of likelihood) either dead, in prison, incognito or not able to find the keys to his wallet.
My personal opinion is that he is incognito; I see him clearly as someone who lives alone with a dog, doesn't like doing housework, grows zucchinis in the summer, hates shoveling snow, has arthritis in his knees, doesn't own a smartphone, his neighbors think him odd, he loves buying discount books at the flea market on Sundays, he's active on the internet under a plethora of pseudonyms and will likely release some of his coins when bitcoin reaches $1,000,000.
There are three possibilities:
1. He still has the private keys.
2. He does not have them or cannot access them (this includes his death without leaving them in inheritance).
3. He got rid of them on purpose, as a donation to the rest of Bitcoin holders. Recall his "lost Bitcoin is a donation."
Obviously I am referring to the million Bitcoins or so attributed to him for having mined them at the beginning. If Satoshi is still alive (or if they are still alive) I am sure he has a good amount of Bitcoin but that nobody links with Satoshi's name.
I think the most likely is option 3. Just as he started up Bitcoin for humanity and stepped away from the project I think at some point he purposely disposed of the keys to those Bitcoins, either for privacy, as a donation, or both. I find it hard to believe that someone as careful as he was would lose the keys and not have multiple backups.
I guess this is mystery which make people curious to know about such situation since many don't know if Satoshi is still alive since until now no one can see his foot tracks or even try to see if there's something suspicious happening to the last wallet address use for his transactions. For now we can't find an exact answers regarding on this question but maybe we can get a hint if someone expose or that can point out that he moves a lot of Bitcoins before he reported gone to the scene and became a mysterious guy in world of cryptocurrency. Many want to find out his identity and his other past activities since maybe it can bring something good to current status of bitcoin.