The girl's relatives at first resisted the adoption but have now consented, the official and people close to the case said. They said her uncle will appear before a judge in the capital Lilongwe on Monday to sign papers.
Madonna is expected to arrive in Lilongwe this weekend. The luxury lodge she normally stays in has been fully booked and visitors are being turned away.
Her spokeswoman Liz Rosenberg in New York has declined to comment on the reports and did not immediately return a call seeking comment Friday.
The popstar's earlier adoption from Malawi sparked controversy as she battled accusations that she used her celebrity status to circumvent Malawian adoptions laws. The adoption of her son David became final in 2008.
It's unclear what legal problems the newly divorced Madonna would now face in Malawi, which does not approve adoptions for single or divorced parents. However, the welfare official has said each case is considered on its merit.
Malawian law is fuzzy on foreign adoptions. Regulations stipulate only that prospective parents undergo an 18- to 24-month assessment period in Malawi, a rule already bent when Madonna was allowed to take David to London.
Rumors that Madonna wanted to adopt a girl from Malawi have been circulating for some time. But the first official hint came from the star herself last week.
In an interview in Malawi's leading daily The Nation, the singer said she was considering another adoption but would only do it if she had "the support of the Malawian people and government."
If the adoption goes through, the 50-year-old singer would become a single mother of four. She also has an 8-year-old son, Rocco, with Ritchie and a 12-year-old daughter, Lourdes, from a previous relationship.
Madonna first traveled to Malawi in 2006 while doing charity work and filming a documentary on the devastating poverty and AIDS crisis there. She is also establishing a school for girls there.
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AP Music Writer Nekesa Mumbi Moody in New York contributed to this report.
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