Madonna chose Cambodia because she liked the way the country handled actress Angelina Jolie's adoption of her son Maddox in 2002, the Sun reported.
Madonna also was reportedly frustrated by the complicated procedures she encountered in adopting her 2-year-old son David Banda from Malawi.
Although her adoption of David is not yet complete, it is expected to be officially approved by April.
Social worker Simon Chisale said in a recent report that David "had bonded well with the Ritchies" and noted it would not be "in the best interest of David" to be taken away from them.
The toddler's relationship with Ritchie was described as consisting of "warm, playful interaction," while Madonna was called a "confident and able parent," the Sun said.
The singer also has an 11-year-old daughter, Lourdes, by fitness trainer Carlos Leon and a 7-year-old son, Rocco, with Ritchie.