One theory that is being floated on Reddit runs like this:
Kleiman is Satoshi, and had the keys to the ~1 million bitcoins. He dies, and his USB stick/computer/whatever went to a relative, who doesn't realize what he is holding. Wright knew Kleiman and knew he was Satoshi. So he invents this crazy story about being Satoshi, but that he can't spend the coins because they are all in a trust that was held by Kleiman.
So now Wright comes public claiming to be Satoshi - and sets himself up to launch a lawsuit against Kleiman's relative to get "his" bitcoins back. If Wright pulls this off, he gains the fabled treasure of 1 million bitcoins off Kleiman's estate.
Thoughts pro and con?
I think this could be plausible if Kleiman is Satoshi. Perhaps Kleiman reached out to Wright knowing that Wright was rich and might have an interest in buying a large amount of BTC as well as the Satoshi identity. Possibly Kleiman was trying to cash out before he died and by saying the BTC was Wright's that would be repaid upon a later date, he was avoiding taxes and living the rest of his days in whatever regulatory nightmare would have come with claiming ownership himself. The 2020 date could even be accurate, as I could see Satoshi wanting to sell to a believer who would hold the BTC until it was stable and not to someone who would dump at a profit and kill the idea. Maybe Kleiman died before everything could be finalized, which would explain why he died poor. That would also explain how Wright became the only one who knew the identity of Satoshi, and why he is trying to set up a case to prove he is the owner of the BTC (which it appears he is not, but maybe would have been if Kleiman had more time).