Answer

It is mentioned in Fatawa Hindiyyah that it is permissible to read the Holy Qur’an whilst travelling or running as long as the place is clean and pure.” (Fatawa Hindiyyah p.316 v.5)

Therefore, if the exercise consists of running or jogging and your mind and concentration is to the words of the Holy Quran, there are no distractions and the place is clean from any impurities then it will be permissible to read the Holy Qur’an whilst exercising.

Only Allah Knows Best