I agree that the kernel module is not restricted to any core but is it possible that whenever it is executed it gives the core number whichever is executing it ?

Have a look at the end of include/linux/smp.h: smp_processor_id() gives you the number of the current executing CPU. get_cpu() will do the same and will also disable preemption so that you will stay on that CPU until put_cpu() is called.

From user-space, you can use sched_getcpu() to obtain the same information.

Hope this helps, Alex.