This comes as the two rival groups of elders in the community have had a frosty relationship, with each side accusing the other of pursuing political interests.
While the holder of the office is expected to unite and provide guidance on the culture and traditions of the Luo community, the divisions began in 2010 after members ousted Ker Riaga Ogallo following allegations of abuse of office.
In revolt against the installation of Opiyo Otondi as Ker, the rival faction led by Nyandiko Ongadi formed a parallel group.
Mr Ongadi, who has accused Mr Odinga of interfering in the activities of the Council of Elders and trying to influence their decisions on key issues affecting the community, has thrown his support behind President Ruto.
Claiming to be the legitimate leader of the group, Mr Ongadi has claimed that no elections should be held to replace Ker Otondi as chairman of the council.
"I will challenge any attempt to elect a new chairman because I have the registration documents of the Luo Council of Elders and no one should claim to lead the group," said Mr Ongadi.
But a member of the council, Mr Odungi Randa, has reiterated that the exercise will continue next week as directed by Mr Odinga, who is their patron.
"We will continue with our election plans, Mr Ongadi is also allowed to continue with his activities as we have no plans to stand in his way," he said, adding that they do not recognise Ker Ongandi's leadership or his position as Ker.
"Let him form his own council and we will not interfere in his activities and he should not interfere in ours," noted the former personal assistant to Kenya's first vice president, Jaramogi Oginga Odinga.
According to Mr Randa, the Luo elders will conduct their activities according to Mr Odinga's instructions.
"We do not know when Mr Ongadi established his office, we have only recognised the instructions given to us by Mr Odinga and from what we understand, Mr Ongadi has his own patron who we are yet to meet," said Mr Randa.
While accusing Mr Ongadi of being pushed by external forces, Mr Randa warned that the move could affect community cohesion.
In an attempt to grab a share of the community that has rallied behind the opposition leader over the past year, Dr Ruto is keen to gain a foothold in one of the community's key pillars as he prepares to seek re-election in 2027.
Last month, during a visit to Kisumu, Mr Odinga held a meeting with elders who agreed to begin the process of electing a new chairman this month.
Mr Odinga had made it clear that the election of a new Ker would begin after the final burial rites of the late Ker Otondi.
Mr Odinga said the burial rites had been delayed following the death of Mama Grace Onyango, the first woman mayor who was also a councillor.
The burial rites, which were to be held at the late Ker Otondi's Nyahera home on Saturday, were however postponed to Sunday following the death of the wife of one of the elders, Mr Randa said.
"We will perform the burial rites on the 11th of June and then on the 15th we will have a panel meeting where we hope to start the process of electing the new chairman," said Mr Randa.
"The panel will be attended by the elders from all the sub-counties and we are also likely to receive the nomination papers," he added.
The 10th Ker of the Luo community will take over a chain of command that began in 1945 when the first modern Luo elder, the late Jaramogi Oginga Odinga, was installed in the same position under the auspices of the defunct but powerful Luo Union East Africa.