Squid is probably the most capable proxy there is so if anything can do it, squid can. Yes transparent is possible though I think it works better for some devices if you just do it as normal configured proxy, squid can be both at same time (listening on multiple ports).
https://wiki.squid-cache.org/Features/SslPeekAndSplice
Might be what you want. I think it's better to avoid all this baloney and just config clients to use the proxy explicitly, unless you're talking about setting this up at a university with 18000 users most of whom don't know which is the "any" key.