The standoff entered its sixth day Sunday and police have said nothing about what demands have been made by Jimmy Lee Dykes, 65, CNN reported.
"We continue to maintain an open line of communication 24 hours a day, whenever he wants to talk," a statement from Alabama State Troopers said.
Officials have been in communication with Dykes through a 60-foot ventilation pipe that leads to the bunker.
Dale County Sheriff Wally Olson said Saturday Dykes allowed authorities to send down medication for the boy's Asperger's syndrome and attention deficit disorder, toys, and potato chips.
The standoff began Tuesday when Dykes got on a school bus in Midland City, Ala., and demanded the driver, Charles Poland Jr. hand over two children.
When Poland protected the children by blocking Dykes' access to the school bus aisle, the gunman shot the driver four times and grabbed the boy, taking him to his hiding place.
A funeral for Poland was scheduled for Sunday, CNN reported.