The couple are said to have been considering the idea for a while, but the footballer has become increasingly keen after visiting the poverty-stricken country two weeks ago.
He spent time at a health clinic, witnessed a birth and joined workers vaccinating children in the community during a four-day trip in his capacity as Goodwill Ambassador for the UN’s UNICEF Children’s Charity.
He said at the time: "I was close to tears. I had to step back and take a deep breath. I'm a very emotional person and I'm even more emotional now I'm a parent."
According to Grazia, the pair have spoken to friend Tom Cruise about his experience of adopting two children with ex-wife Nicole Kidman.
A friend is quoted as saying: "Adoption is something David has been talking about for some time. Tom has talked to David about how adoption changed him and how he’s been able to change the lives of two amazing children.
“If there is one subject that can move him to tears, it’s the thought of being unloved, uncared for and with no hope or future.”
The source added: "It’s clear they both think adoption is great.”
However, a spokesperson for the Beckhams dismissed the claims, saying: "They both have said that they admire people who go through the adoption process, their focus is raising their own three boys."