If that computer is in the same network (wifi, lan) you can use wireshark.
If the computer is not in a network to which your sniffer has access to, than you have to install a sniff and log program on that computer that would periodically compress and send a package with logged addresses to you.
You can download the first suggested option (WireShark) from their official website: https://www.wireshark.org.
The second one, you would have to write on your own or find one if available on-line. It could easily be written, depending on the target platform, system and architecture.