Norfolk Southern owns the bridge and must give the go-ahead to have it torn down.
"City officials brought this to our attention two weeks ago," said Rudy Husband, spokesman for Norfolk Southern. "Right now we're just in the process of exploring various options. We are going to work with the city and come up with a solution that works for everybody."
The bridge for years has been the turf of homeless people who refuse to stay in area shelters, police said. Numerous tents have popped up on the bridge, though police on more than one occasion have tried to chase the vagabonds off.
Norfolk Southern officials were reportedly taken aback by the conditions on the bridge and are open to having it torn down, city officials said.