When the Russians go "as far" as saying "based on", then given examples of recent developments (meaning anything post-soviet) this means, its a modified Tu-160. Because if it really would be a new project, involving a new design off the drawing board, the usual language used in Russia involves expressions such as "revolutionary" or "unmatched" etc. The whole thing sounded very down-to-earth when it was announced.Even if its the TU-160 it may not look anything like the TU-160. The structure of the TU-160 is the floor and not the body so it could look drastically different. If its based on the flying wing then things get interesting.
I agree that everything is just speculation at this point in time. But claims involving a completely new design have no grounds in reality. The announced first flight-date of 2015 certainly does not support this (even when the usual Russian optimism is being considered). It would however fit quite well with some modification work being done on the Tu-160 platform.