Alan Greenspan, the former Federal Reserve chief who called out the tech-fueled rally of the mid-1990s as "irrational exuberance," is now giving investors a new warning.

In a CNN interview, Greenspan said it was unlikely that the current market would stabilize and then take another big leg higher. "It would be very surprising to see it sort of stabilize here, and then take off again," Greenspan said. Markets could still go up, but "at the end of that run, run for cover."

Greenspan told CNN the bull market is over, pointing to how stocks have fumbled in recent days. On Tuesday, stocks rallied but they tumbled on Monday and have been in a decline since October, weighed by concerns over global trade conflict and slowing global economies. The S&P was on track, as of Monday's close, for the worst December since 1931.