The body of a female athlete was found with stab wounds in the town of Iten, famous for its centre for long-distance runners.
Police say they are looking for the boyfriend of a woman who competed in a sport.
She is the second female athlete to die in Iten.
The killing of an Olympic runner shocked the country.
Her husband is in custody and denies murdering her.
Tom Makori, the police chief in Iten, told the news agency that the body was found in a state of decomposition.
Police say that her boyfriend may have left the country because he was training at the same high-altitude centre as her.
The suspect called a friend who was training with him and told him that he had killed a girlfriend and the body was in the house, according to Mr Makori.
As a junior athlete, Mutua competed for Kenya but later switched to run for Bahrain.
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