Is there any DNS system or Service that is HTTPS aware?

This isn't possible with DNS. The DNS request is completely independent of the reason for the request.

For this to be possible, the entire caching system for DNS would have to be scrapped. DNS would also have to be rewritten every time a new scheme was invented.

What are you trying to do? There might be a better way to solve your actual problem.

No.

DNS is not aware of HTTP or HTTPS.

Compare it to asking for secretary the phone number (IP number) for someone. You will get the same reply, no matter what you wanted to ask the person on the other end.

As everyone has mentioned, you can't do this with DNS. I think this is typically done with URL redirects. For example, if you're using Apache as your Web Server you can do set up redirect rules with mod_rewrite. Then you can write rules like:

# If HTTPS redirect to special.domain.com
RewriteCond %{HTTPS} =on
RewriteRule .* https://special.domain.com%{REQUEST_URI} [R,L]

# If not HTTPS redirct to simple.domain.com
RewriteCond %{HTTPS} !=on
RewriteRule .* http://simple.domain.com%{REQUEST_URI} [R,L]

Here are some more examples: http://www.askapache.com/htaccess/ssl-example-usage-in-htaccess.html

I'll give you the benefit of the doubt and assume that:

• You're familiar with the OSI model, and the fact that DNS, HTTPS, and HTTP are all application level protocols.
• You understand that protocols must be independent (both across layers and within layers) in order to be useful.

I therefore take your question to mean that you're wondering if there is an HTTP/HTTPS analogue in DNS to the MX (mail exchange) resource record (RR) among the resource record types supported by DNS.

This appears to be the purpose of the SRV (service) record type, described in RFC 2782. although it appears that LDAP, SIP, and XMPP services are more commonly advertised this way via DNS.

The reason for this appears to be historical: SRV records were proposed, implemented, and deployed only after HTTP was proposed, developed, and deployed. For some discussion about why it may not be a good idea to use SRV records to advertise HTTP/HTTPS at this point, see this question.

No, DNS doesn't know (or care) which protocol is requesting the lookup.