All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad , is His slave and Messenger.
As far as we know, there is no authentic narration from the Prophet , that precisely prohibits talking or reciting the Quran when the Athaan is being called. However, we are ordered in the Sunnah to repeat the words of the Athaan after the Mu’aththin (the person calling the Athaan) as we mentioned in Fatwa 92196.
There is no doubt that talking or reciting the Quran when the Athaan is being called makes it impossible to revive the Sunnah of repeating the words of the Athaan. There is no doubt also that repeating the words of the Athaan when one hears it [Athaan] comes in priority over reciting the Quran because repeating the words of the Athaan is a timed act of worship that Allaah legislated when one hears it. Reciting the Quran at this precise time preoccupies one with another act of worship instead of being preoccupied by the legislated act of worship.