Can SQL Express be used as a Log Shipping monitor server? I'm keen to setup a "Monitor Server".

We have SQL 2008 R2 Enterprise edition on both primary and secondary servers.

Can we use SQL Express in monitoring server setup for licencing purposes?
No, log shipping is not supported on SQL Express 2008 R2, even as the monitor.

The official MSDN page does not state this explicitly, but I found this case where someone tried to use Express and got an error.

If you have either a Workgroup or Web edition licence lying around unused, those support what you need, as well as Standard (and higher).