Did the Buddha mean this by "rebirth"?

I suspect the Buddha used the term "rebirth" in a sense different from its traditional meaning. Probably he meant that our **sense of separate self** is repeatedly being born, decaying, dying and being reborn until we attain Nirvana. In this sense, rebirth happens only in our **present life and not after our physical death**. Is there any evidence in the early canon to support that the Buddha used the term "rebirth" in the above sense?