The earliest such quote I could find was from Windows on the Future: Education in the Age of Technology by Ted McCain, Ian Jukes, (2001, p. 80):
the Secretary of Education, Richard Riley in the Kentucky Teaching and Learning Conferences in Louisville on March 2, 1999, was quoted as saying that none of the top 10 jobs that will be available in the year 2010 exist today, and that these are jobs that will require workers to use technology that has not yet been invented to solve problems that we have not yet thought about.
They didn't give any source for their quote. But given how specific they were about when and where this was said, this quote is perhaps somewhat trustworthy.
Instead of directly quoting Riley, you can just quote the above sentence by McCain and Jukes like so:
According to McCain and Jukes (2001), Richard Riley stated "that none of the top 10 jobs that will be available in the year 2010 exist today, and that these are jobs that will require workers to use technology that has not yet been invented to solve problems that we have not yet thought about."
Note: The quote probably became popular with this video first released in 2006 by Karl Fisch (accompanying blog).