(a) It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "Only one who has ablution should give the adhan."
(b) It is narrated from al-Zuhri that Sayyiduna Abu Hurayrah (may Allah be pleased with him) said: Only one who has ablution should call the adhan for the prayer.
Mu'awiyah bin Yahya al-Sadafi, who narrated it in this way (as the Prophet's words), is da'if (weak); the correct version is the narration of Yunus bin Yazid al-Ayli and others from al-Zuhri, as the words of Abu Hurayrah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 1858
(a) Abd al-Jabbar bin Wa'il (may Allah have mercy on him) narrates from his father (may Allah be pleased with him) that it is a right and the Sunnah that only one who has ablution should give the adhan, and standing. (b) Abd al-Jabbar bin Wa'il (may Allah have mercy on him) narrates from his father (may Allah be pleased with him) in a mursal form. This is the view of Ata' bin Abi Rabah (may Allah have mercy on him). Ibrahim al-Nakha'i (may Allah have mercy on him) said that they saw no harm in giving the adhan without ablution; this is also the view of al-Hasan al-Basri (may Allah have mercy on him) and Qatadah (may Allah have mercy on him). But giving the adhan with ablution is recommended (mustahabb); this has already passed in the Book of Purification (Kitab al-Taharah).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 1859