If I understand you correctly, you want to capture the traffic to a 3rd party site you have no control of. For example the site of a competitor.
Short answer: No. It's not possible to build a sniffer locally, that captures the requests to a 3rd party site located somewhere else.
Long answer:
To sniff all the packets going to a server/site, you have to be on the route, that all these packets use. If you are not on the route, you simply can't see them.
So the only option would be to gain control of some network infrastructure like switches or router, that are very close to the target server/cluster/site (so all or at least many of the packets use this route) or gain control of the target server(s). Both is obviously illegal.