I think you have here is an X-Y problem.

You want to select the source IP address but you ask how to select the interface.

Selecting the interface is difficult but selecting the IP address is easy. You use bind().

You don't say which Syslog module you are using so I will assume Sys::Syslog. I've looked in Sys::Syslog and it's pure Perl so although it does not currently take a source IP address argument you could easily hack it to set the source IP address of the socket between creating and connecting.