Can we monitor asterisk by using Nagios?

Is it possible to monitor the Asterisk by Nagios?

Your question is not specific.
Which parameters / events do you need to monitor?

Nagios can do a lot for you, but for many parameters you would have to write scripts…

Almost Everything related to asterisk i.e live calling channel and free channel, PRI/SIP/VOIP registration status etc

You could try SNMP.