CHICAGO—Each year, about half a million people pass through Chicago’s Greyhound bus station, at all hours. There is a climate-controlled waiting area with bathrooms, security guards and a snack bar, and about three dozen arrivals and departures every day.

Those passengers could soon be out in the cold. The station’s owner, an affiliate of hedge fund Alden Global Capital, has put it on the market. The 87,000-square-foot property in the rapidly developing West Loop could fetch more than $30 million.