He also urged Kenyans to support the dialogue process.
Gachagua had sworn to ensure the removal of Justice Maina whom he accused of being corrupt after she declared his fortunes as proceeds of crime. He claimed the move was meant to soil his image.
"On Thursday, this coming week at 2.15 pm, I will personally present a petition before Lady Chief Justice Martha Koome against Justice Esther Maina for her removal from the Judiciary," Gachagua said in Eldoret last weekend.
He claimed that Justice Maina had not given him an opportunity to be heard and that she also rejected his plea to cross-examine the investigator in his case.
The deputy president was referring to the occurrences of 2022 when the High Court ruled against his application to have his accounts unfrozen by the Assets Recovery Agency.
The court then ruled that Gachagua forfeits to the State Sh202 million , terming the money as proceeds of crime.
The Asset Recovery Unit had flagged Gachagua's three personal accounts over "huge suspicious" debit transactions amounting to Sh7.3 billion. Gachagua however got his money back after he and President William Ruto took over the reins of government in 2022. The Anti-Corruption court threw out the case over the lack of evidence.
The statement by Gachagua comes days after Koome said she was ready to meet the Head of State to discuss the dispute between the Judiciary and Executive following weeks of a sustained onslaught by President Ruto.
On Monday, Koome revealed that the Judicial Service Commission had written to Ruto, requesting for a meeting to discuss alleged graft in the Judiciary.
"We will be looking out for that dialogue with the president. We have written to him and I believe that the president is going to give us an appointment," she said.
And in response, Ruto, who was speaking during the commissioning of the Tinderet Integrated Technical and Trainers College in Nandi County on Tuesday, welcomed Koome's invitation for dialogue .
He said he would steer the deliberations in a set up that would involve the Legislature, Judiciary and Executive.
Notably, for the better part of this year, the president and the Judiciary have been embroiled in a standoff, with the former accusing the latter of being in cahoots with the opposition to frustrate the government's development agenda.
Ruto has sustained his attack on the Judiciary over his affordable housing project. While Ruto is adamant that his flagship project is poised to create over 10,000 jobs for the women and youth, the courts have declared unconstitutional a levy introduced by his administration to facilitate the construction of the houses.
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The imminent talks have however raised questions, with some observers warning that any meeting between the two arms of government would undermine the Judiciary's independence.
Questions have also emerged about what legal structures will be used to conduct the discourse.
Opposition leader Raila Odinga earlier this week, warned that Koome's meeting with President Ruto would not only compromise the Judiciary but also the country.
"There is no need to engage with the Executive. If you want to compromise the Judiciary and negotiate with the Executive on these kinds of disputes, then you are going to compromise the whole country," said Raila.
Wiper leader Kalonzo Musyoka also waded into the matter saying that he was not convinced that the talks would yield anything much. During an interview on spice FM on Wednesday, Kalonzo said the meeting not only undermines the independence of the judiciary but raises suspicion.