Reference: http://www.alfawzan.af.org.sa/node/14987
Question: If I was reading the Qur.aan, and someone came along and conveyed the salaam [greeting] to me, should I respond to his salaam or should I [first] complete [reading] the aayah?
Response: [You should] complete [reading] the aayah, then reply to his salaam [when you have finished doing so]. [Note that] it has not been legislated to convey the salaam to the one reading the Qur.aan, because doing so will busy him and interfere with his reading; [instead], when he has finished reading – then convey the salaam to him.
