Two out of three judges considering the case have allegedly submitted reports recommending the adoption, while the third is said be "in complete unison with them".
A source told The Sun: "The paperwork is being typed up now".
"All recommendations are in favour of the adoption taking place. Mercy should start packing her bags. She's off to America."
The 50-year-old star appealed after her two-year application to care for the little girl was rejected on the grounds that she hadn't been resident in the African country for 18 months. One of the judges apparently deemed the rule out of date.
A friend of Madonna's said the singer was "ecstatic", adding: "She made a promise that she wouldn't give up on Mercy and, believe me, she could move mountains when she's this determined."