SIP Chat Server And Asterisk

Please, Is this possible?

I have asterisk server with list SIP clients registered to it. Is there a way these SIP Clients can chat with each other using
an xmpp server ( like openfire).

1. I do not have need for any other client except SIP client.
2. My SIP client has only once SIP account.
3. I am considering a chat server because, I want users to get messages sent to them, when they were offline immediately they are back online.
4. Alternatively, Is there a SIP Chat Server that works with asterisk ?

Any help will be appreciated.

I would put Kamailio in front of your asterisk server, then you can chat and make phonecalls .

Take a look here: