Muharib bin Dithar (may Allah have mercy on him) said: A Mother of the Believers died, I think it was Sayyidah Maymunah (may Allah be pleased with her), and she left instructions that Sa'id bin Zayd (may Allah be pleased with him) should lead her funeral prayer.
Sufyan al-Thawri narrated it from Ata bin al-Sa'ib, from Muharib bin Dithar, that Umm Salamah (may Allah be pleased with her) left instructions that someone other than the ruler should lead her funeral prayer; and this is more correct.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الجنائز / 6898
Abu Ishaq (may Allah have mercy on him) said that Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) left instructions: "When I die, Sayyiduna al-Zubayr bin al-Awwam (may Allah be pleased with him) should lead my funeral prayer."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الجنائز / 6899
Khuza'i, (a son) of Abdullah bin Mughaffal (may Allah be pleased with him), said that Abdullah bin Mughaffal (may Allah be pleased with him) said: "Let my companions take charge of me, and let Ibn Ziyad not lead my funeral prayer." He said: Those who took charge of him were Abu Barzah and A'idh bin Amr (may Allah be pleased with them both), and some people from among the Companions of the Messenger of Allah (peace and blessings be upon him) (may Allah be pleased with them).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الجنائز / 6900