The eminent Muslim scholar and renowned Da`iyah, Sheikh `Abdel Khaliq Hasan Ash-Shareef, states: “Du`aa’ during prostration in Prayer is always encouraged whether the Prayer is fard or nafila. Abu Hurairah (may Allah be pleased with him) related the Prophet (peace and blessings be upon him) as saying: “The nearest a Muslim is to his Lord is while he is in prostration. So, make Du`a in it.” (Reported by Muslim, Abu Dawud and An-Nasa’i)
There is nothing in the hadith or the Sunnah restricting this hadith to making du`aa’ in only nafl Prayers.
However, what is prohibited is reciting the Qur’an in ruku` or sujud. the Prophet (peace and blessings be upon him) said: “I have been forbidden to recite Qur’an when bowing and prostrating. As for ruku’ (bowing), glorify your Lord therein, and as for sujood (prostration), strive in du’aa’, for then it is more likely that your Lord will answer you.” (Muslim, 738). But if you recited any du`aa’ from the Qur’an during ruku` or sujud, it can be considered as du`aa’ rather than a recitation of the Qur’an.”