Is there any harm in concentrating on the breathing process while doing physical exercises such as gym?
Aum Guru !
There is no harm at all in concentrating on the breath as you work out. In fact, it is a good thing to do.
Depending on what your workout is, however, there may be an even better point of focus: the energy with which you exercise.
For example, if you lift weights, then concentrate on the subtle energy that enables you to do that, rather than on the weight itself. Then you will not only exercise your muscles; you will also build your inner awareness of something much more important: life-force.
So yes, pay attention to the breath, because there are better and worse ways to breathe when you work out. But once healthy breathing becomes an ingrained habit, give your primary attention to your life-force.
Blessings on your workouts (and work-ins),