The Federation of Women Lawyers wants President Kenyatta to appoint at least seven women to his Cabinet for his second term, and is prepared to give him a list of those it thinks are qualified.
Ms Josephine Wambua-Mongare, the chairperson of the FIDA-Kenya cited the constitutional requirement that not more than two-thirds of elected and appointed leaders be of one gender.
"The women of Kenya call upon you to uphold the spirit and letter of the Constitution. We look forward to at least seven Cabinet seats assigned to competent and qualified women," Ms Mongare said in an advertisement in the Nation.
"FIDA-Kenya is prepared to furnish you with a list of women who fit the profile of a Cabinet secretary in any of the available 22 positions."
She said the inclusion of more women should apply in the assignment of other state jobs as it would guarantee women's right to equity and equality and ensure they are included in decision-making.
The FIDA-Kenya chairperson said the organisation is among those anxiously waiting for the announcement of President Kenyatta's new Cabinet, which has since the Supreme Court's affirmation of his victory been the subject of plenty of speculation.
"The women of Kenya are cognisant of the various calls advising you to allocate Cabinet seats advised on different criteria-- including political allegiance, tribal inclusion, reminder of campaign promises, rewards for support to your government and claims of track records," said Ms Mongare.
Lobbying and speculation over the men and women who will form the next Cabinet have intensified over the past week after President Kenyatta was sworn into office.
The President has also been carrying out appraisals of the Cabinet, with the Secretaries reportedly put to task over their achievements over the past four and a half years.
There are currently five women in the Cabinet: Raychelle Omamo (Defence), Phyllis Kandie (East African Community, Labour and Social Protection), Sicily Kariuki (Public Service, Youth and Gender Affairs), Amina Mohammed (Foreign Affairs and Trade) and Prof Judi Wakhungu (Environment).
Anne Waiguru and Charity Ngilu were in the first Uhuru Cabinet.
Ms Waiguru resigned under pressure after the discovery of corruption at the National Youth Service, which was under her docket, while Ms Ngilu was forced to leave in March 2015 after she was named in a list of public servants under investigation by the Ethics and Anti-Corruption Commission.
Both have since been cleared and are now governors - Ms Waiguru in Kirinyaga and Ms Ngilu in Kitui.