Reference: http://www.alfawzan.af.org.sa/node/16867
Question: [What is the ruling regarding] reading the Qur.aan during the tawaaf and the sa’ee, whilst doing ‘umrah on behalf of my mother?
Response: There is no harm in that; you can supplicate to Allaah (Jalla wa ‘Alaa) during the tawaaf with legislated supplications – and that is best, or you can read the Qur.aan. You may also remain silent for the duration of the tawaaf – without supplicating, and your tawaaf is sound. However, [by doing so] you have left a recommended act from those which have been recommended for during the tawaaf – and that is to supplicate during it.