According to 'Sky Sports' Eriksson met with officials from the Iraqi FA in Istanbul last week, and decided against taking the deal.
They reportedly offered the former England manager a three-year deal, which would have taken Iraq past the World Cup qualifiers and the Asia Cup.
The 70-year-old could now turn his attention to the prospect of becoming Cameroon's new coach.
The Cameroon Football Federation (Fecafoot) met with Eriksson last week to discuss the opportunity to replace Hugo Broos as head coach.
Fecafoot said: "After the interview with Sven-Goran Eriksson and taking into account the other existing offers, Fecafoot will reveal in the next few days its choice of permanent coach for our national team."
Eriksson enjoyed success as a club coach throughout Europe, before being made manager of England who he was in charge of between 2001 and 2006.
He also coached Mexico, and led the Ivory coast to the South Africa World Cup in 2010.