What OS is your Glassfish server running on?
If Linux do you have rsyslog available? If you do you can configure it to read the local log file and forward it to a syslog host. If rsyslog is not available Logstash is an option. If Glassfish is running on Windows you can use a forwarder such as NXlog or Logstash to read the local file and forward to the syslog server.