The women, aged 82 and 61, were found dead at an apartment complex at 1221 Main St., where Varner lives, according to a statement from Antioch police. Police would only say they want to question Varner.
"He was an older man who didn't have much of a job and didn't have a lot of money and his mother was in a wheelchair and he took care of her. And, he used to shovel snow for us and salt, and he would look out for the property for us," Nancy Kiefer, landlord, said.
Police hauled dumpsters out of the apartment parking lot Tuesday. Neighbors say they've seen Varner hanging around the area and don't think he would have gone far.
"When I tried to sleep last night, it was difficult to sleep. I was up all night. I was running to the window with every noise I heard. This morning, when the dumpster was moving, I thought someone was rifling through the garbage to try to get some evidence this morning. I was freaking out," Felicia Johnson, neighbor, said.
Varner was last seen driving a 2002 tan, Chevy extended conversion van with Illinois license plate N94-3872. Police said the van had damage to the passenger side's taillight. Neighbors said it was in the parking lot Monday.
Anyone who spots Varner should call 911.
The Sun-Times Media Wire contributed to this report.