The USSR was issued a country code top level domain prior to it's collapse. They certainly must have known about the internet at that point (and probably before) so were there any plans regarding it's deployment and use within the USSR?
Just to clarify, are you asking about the Internet (the networked global computing infrastructure, developed after 1969) or the World Wide Web of hypertext and html, developed after 1989? The USSR absolutely had a presence on the Internet, but the Web was in its infancy when the Soviet Union collapsed.