Officials told AFP that Elton John may not be able to adopt a Ukrainian orphan because the country's legal system only allows foreigners to adopt if they are married.
Sir Elton "does not have the right to do it because there are certain obstacles which cannot be overcome," said Lyudmila Balym, an official at the ministry for family.
Ukrainian law stipulates that foreign adoptive parents must be married couples and homosexual marriage is not recognized in the country.
Ukrainian law also says the age difference between adoptive parents and the child must not exceed 45 years, Balym said, meaning Sir Elton, 62, and Furnish, 47, also fail to meet this criteria.
Sir Elton said on Saturday he wanted to adopt a 14-month-old boy he had met in a Ukrainian orphanage, saying the youngster called Lev had "stolen his heart".
He met the toddler while visiting the country with his AIDS charity foundation. He gave a performance for children at the orphanage, some of whose parents had died of the disease.
Sir Elton follows a long line of celebrities and pop stars looking overseas to adopt a child and he is not the first to find his private life a problem.
US pop diva Madonna's attempts to adopt two children in Malawi have sparked heated debate, while Angelina Jolie, Tom Cruise and Nicole Kidman have also made headlines by trying to adopt children from impoverished countries.
US actress Mia Farrow adopted 10 of her 14 children in countries ranging from India to South Korea and Vietnam.
Sir Elton's adoption bid has already sparked heated debate in the young boy's homeland, with some expressing shock at the idea of allowing a child to live with a gay couple.
It will not be possible to confirm whether the toddler is HIV positive until he reaches the age of 18 months, said staff at the orphanage, which is in the eastern city of Makeyevka.
But others supported the idea and said it could give the youngster the chance of a better life.
"Why not? At least the child will have a normal life," said Lyudmila Batikhina, a medical assistant at the orphanage.
Irina Kuzmenko, a student in the city of Donetsk said she envied the boy for being picked out by the wealthy singer.
"Does it really matter who your parents are as long as they love you?" she said.
"I want him to adopt me too," she joked.
Ukraine has one of the fastest rising HIV rates in Europe.
Two years ago Sir Elton gave a free concert in the main square in Kiev attended by tens of thousands of people to raise awareness of HIV/AIDS in the country.
The star has sold more than 250 million records worldwide, with 29 consecutive Top 40 Hits and 35 gold and 25 platinum albums.