Log4j doesn't allow to catch stdout and stderr messages out of the box. However, you can still intercept them with a custom output stream, which is especially useful when you have to log data that third-party libraries write to the standard streams.
This has already been done by Jim Moore (have a look at the LoggingOutputStream in the log4j source code). The issue is that this LoggingOutputStream requires org.apache.log4j.Category and org.apache.log4j.Priority which are now partially deprecated.