City inspectors found 22 violations at the property, including pest infestation and an unstable roof, The Cleveland Plain Dealer reported Friday.
Sowell was convicted in August and sentenced to death for kidnapping, murder, abuse of a corpse and other crimes against 11 women whose remains were found in and around the property at 12205 Imperial Ave., which is owned by the estate of Sowell's stepmother and a reverse mortgage company.
Cleveland City Councilman Zack Reed said the house should be destroyed. He would like to see it replaced with a neighborhood memorial, the newspaper said.
"It's a long time coming and I hope that it will continue to heal the wounds of a broken community," he said.