A base station, a terminal device, a control method, and a program for communication handover are provided. First information indicating one or more base stations which are candidates for a handover destination of a terminal device in connection from a base station, is acquired. Second information regarding communication quality predicted in a communication through a candidate base station for each of the candidate base stations is acquired based on the first information. Third information regarding the communication quality for at least one of the candidate base stations is notified to the terminal device based on the second information. The third information is used to handover of the terminal device.