The Welshman was one of six applicants interviewed for the job and it is understood he was offered the position last week.
Holley, who frequently appears as an analyst on BBC Wales, said: "No head coach position should be taken for granted . . . and I am flattered and honoured to have received the Connacht offer.
"However, my decision is based purely on the timing and my current personal circumstances."
Connacht interviewed a six-man shortlist understood to consist of former Wasps and Sale coach Tony Hanks, former Wasps player and current Clermont assistant coach Alex King, former Samoa player and Auckland coach Pat Lam, current Connacht assistants Billy Millard and Dan McFarland and Holley.
Lam has emerged as the favourite for the post.