Abu Malik al-Ashja'i (may Allah be pleased with him) reports from his father that he prayed Fajr with the Messenger of Allah (peace and blessings be upon him), and he (peace and blessings be upon him) did not recite the qunut.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3877
Abu Malik al-Ashja'i (may Allah have mercy on him) says: I asked my father about the qunut, and he said: I prayed behind the Prophet (peace and blessings be upon him), Sayyiduna Abu Bakr, Sayyiduna Umar and Sayyiduna Uthman (may Allah be pleased with them), and I did not see any of them ever recite the qunut.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3878
(a) Al-Aswad and Amr bin Maymun (may Allah have mercy on them both) say: We prayed Fajr behind Sayyiduna Umar (may Allah be pleased with him), and he did not recite the qunut.
(b) In the chapter on qunut we have already narrated from the Messenger of Allah (peace and blessings be upon him) and from the Rightly Guided Caliphs (may Allah be pleased with them) that they recited the qunut in the morning prayer. It is reported with sound chains from Sayyiduna Umar (may Allah be pleased with him) that he used to recite the qunut in the morning prayer. If these people omitted the qunut on some occasions, whether through forgetfulness or deliberately, this indicates that it is not obligatory; and since it is not reported from any one of them that they performed the prostrations of forgetfulness, this indicates that forgetting the qunut does not require the prostration of forgetfulness. And Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3879