Without additional code that is not possible in Java.
Regarding that requirement you could either go with a approach as @khelwood mentioned, but in that case you would have to adjust the caller code (which might or might not be tricky).
I would consider the use of aspectj. That way could would not have to change any code and create a pointcut guarding all your setter of your model class. The apsect itself could keep track of which methods where called on which object. The code would have to be written with care though since threading could be an issue.
This approach is way more complex but depending on your scenario it might be worth the effort.
Another thought
You maybe just initialize every field with a constant you recognize as "undefined". You would just have to make sure, that those values CANNOT be set by the "real" application.