ODM had nominated MPs Mishi Mboko (National Assembly) and Okong'o Omugeni (Senate) while Wiper nominated Patrick Makau.
They claimed that according to law and the Azimio agreement, the slots were to be shared out so that both ODM, Jubilee, and Wiper parties got one slot each.
They threatened to walk out of Azimio if the matter was not resolved.
National Assembly Majority Leader Kimani Ichungwah will table the names of Nyandarua Woman MP Faith Gitau, Nyali MP Mohammed Ali, Laikipia Senator John Kinyua and Nominated Senator Joyce Korir who are members of the ruling Kenya Kwanza Alliance.