Ayacko and his entourage were holding meetings with ICC president Eshan Mani and chief executive Malcolm Speed to press for recognition of a new governing board for Kenyan cricket, Cricket Kenya, that the government appointed after disbanding the Kenya Cricket Association (KCA) for financial mismanagement.
"They are keen to impress on the ICC to cease working with the KCA," a Kenyan sports ministry official said.
"Cricket Kenya is approved by the Kenyan Cabinet as the legitimate body and must now seek affiliation with the ICC."
Kenyan cricket was thrown into disarray after the government dissolved the KCA in January and appointed a caretaker committee which it later replaced with Cricket Kenya.
Despite getting the support of the government and majority of local cricket clubs, the new board appears not to have won backing from the ICC which still recognizes the KCA as the legitimate body to run the sport in the country.
The confusion surrounding the administration of the sport prompted the ICC to postpone Kenya's Intercontinental Cup match against Namibia last week.