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?
I suspect the Buddha used the term "rebirth" 


The entire premise of your question is faulty, unfortunately. The Buddha never, afaik, used a term that could be translated as "rebirth". In fact, the idea of anything being reborn goes against orthodox early Buddhist teachings. Throughout the Buddha's teachings, it is made clear that at the breakup of the body there is birth, not rebirth - as in birth of new things, not the return of anything old.


  Probably he meant that our sense of separate self is repeatedly being born, decaying, dying and being reborn until we attain Nirvana. 


Since the Buddha never taught the idea of self and denounced any view of self as leading to suffering (MN 22), this is highly unlikely to be correct.


  In this sense, rebirth happens only in our present life and not after our physical death. 


To repeat, according to early Buddhism, rebirth never happens. In this life, there is what is called khaṇika-maraṇa - death of a moment. Each momentary experience is born and dies, never to arise again. At the moment of conceptual death (sammuti-maraṇa), this process of momentary birth and death continues unimpeded unless one has experienced "death by cutting off" (samuccheda-maraṇa) - i.e. of the defilements (q.v. Vism VIII.167) - in which case there is no further arising.

To put it succinctly, physical death isn't even real according to early Buddhism; it is a concept based on the artificial construct of a "being" who is "born".


  Is there any evidence in the early canon to support that the Buddha used the term "rebirth" in the above sense?


No.