Alden was detained following the fatal shooting of Grace Wangeci at his home, the 53-year-old suspect claims a pistol that Wangeci, 42, was holding went off while she was taking "selfies".
Alden said she shot herself by accident and has denied responsibility for her death
It is believed the British national was in a relationship with the woman who lived in South C and owned a recruitment bureau.
Alden has been in the country since 2015. His work permit will expire in December 2017. The ex-chief executive is a licensed gun holder.
Police said he was arrested after an examination found Wangeci's body had a gunshot wound, fresh stab wounds and broken fingers.
Richard Alden has appeared in court where authorities ordered he should be held for another five days.