Create new @me.com mail account (2016)
Since mobileMe (which handed out the @me.com addresses) was turned off some time ago, all you can now create are @icloud.com emails. If you had an AppleID which predates mobileMe (e.g. a dot Mac account) you would have three aliases:


myname@mac.com
myname@me.com
myname@icloud.com


So the short answer is, no it is not possible to create a new @me.com email address anymore.

More official info on this here: https://support.apple.com/kb/HT201771