I saw this question on Quora. I know that Snape isn't the master of the Elder Wand. Draco is the master when he disarmed Dumbledore. But later it passes to Harry as he himself disarmed Draco at Malfoy Manor. When Voldemort asks Snape about the Elder Wand, did Snape know at that time that it belonged to Harry?
He probably hadn't even considered it.
Voldemort only discovered (and Harry by extension) that Dumbledore possessed the Elder Wand days before the Battle of Hogwarts.
Snape would have had no reason to speculate about Dumbledore's wand before then, even if he did know about wandlore, as he would have had no reason to think about looting from the corpse of someone that he was very close to.
I'm not sure if Voldemort would have told Snape that the wand he retrieved was from Dumbledore earlier than the moment right before killing him, so it's possible that Snape never got the chance to mull that idea over very much when he was staring imminent death in the face.
Even if Snape knew right around the time that Voldemort did, Voldemort certainly wouldn't have admitted weakness in himself by admitting that the wand was resisting him, up until the boathouse where he had already resolved to kill the only person that he told.
So, at the very most, we can say that Snape might have suspected that he himself, or Draco, might be the master of the Elder wand in the days between Voldemort getting the wand and the Battle of Hogwarts.
However, if in this time frame Snape had considered that killing Dumbledore would make him the master of the wand, he would know that he was in danger of being killed by Voldemort, and as it was still necessary for him to provide Harry with the information of him being a Horcrux I think he might have made more of an effort to get that information to him.
If he knew that it was Draco that had become the master of the wand by disarming Dumbledore, he would likely have warned him about being in danger. He wouldn't want to see his favorite student, and someone he has looked out for for a long time, potentially being on the wrong side of the Dark Lord, considering that Voldemort doesn't seem to be the type to disarm someone in order to get the power that they have.
There is no way that he could have known that Harry was the wand's owner, as he wasn't at Malfoy Manor when Harry disarmed Draco, and I don't think that anyone who was there would have provided him with such trivial information.
So all the evidence points to the fact that he didn't know who the true owner of the Elder wand was, or that he ever gave it a moment's thought before the conversation in the boathouse, at which point it was already too late for him to seriously think it through.
I think at best, Snape would know he himself is not the master of the Elder Wand. If he understood wandlore, he would know that simply killing Dumbledore would not transfer the wand's loyalty to him. Also, since Snape arrived at the platform of the tower and found Dumbledore wandless, Snape would have no idea who disarmed Dumbledore (if anyone did).
If Snape did not know wandlore, then he would have no clue as to the master of the Elder Wand. I can easily imagine Alan Rickman saying "no idea..." :-)
I don't think Snape knows Harry is the new owner. Because as we all know, Snape is a Legilimens (meaning he can read minds as long as he wants to). Since Harry nor Draco know who the real owner is, even though he read their minds, he'll get nothing.