"This is a viral response," said Corey Lada with the Kansas Children's Service League. "And it's pretty insane."
Since the children's profile was first featured in the Kansas City Star on Saturday, the state's adoption service has received thousands of responses.
Officials say the ad has triggered interest in adoption across the state.
The article featured two sisters and three brothers, ages 2 to 11, who are identified by their first names only.
It describes their interests and hobbies, which range from music and sports, to hip-hop dance and collecting Pokemon.
The children are all currently being kept in separate foster homes, Mr Lada said, but they hope to be adopted together.
He declined to provide more information about the children's situation.
Theresa Freed, with the Kansas Department for Children and Families, told ABC News that the agency has received more than 1,300 emails about the children.
"We've identified some possible families who may be a good fit," she said..
The state adoption website, adoptkskids.org, has had to take down the family's profile, after interest overwhelmed the website.
Mr Lada said the state has been struggling to respond to public interest, and he asks that people be patient as staff members try to catch up.
"It's a great crisis to have," he said.
A US newspaper's "Family Wanted" ad featuring five siblings up for adoption has received a massive response and sparked a huge number of offers.