The last time America, the world's No.1 economy experienced such an episode was in the 1970s and early 1980s. Stagflation occurs when the economy suffers from high inflation and high unemployment.
"How long it lasts or how big it gets, it's too soon to tell," Greenspan told CNN.
"We'll know it when we get on top of it," 92-year-old Greenspan, who headed the Federal Reserve from 1987 to 2006, said.
Greenspan's interview was aired Tuesday, a day before current Fed Chief Jerome Powell announces another possible interest rate hike and the US central bank's outlook for 2019. The Fed has been trying to restore rates to more normal levels after a decade of historic lows.
Greenspan, who famously warned more than two decades ago about "irrational exuberance" in the stock market, also said the party's over on Wall Street.
Critics, including many economists, now blame the former Fed chairman for the 2008 financial crisis for having encouraged the bubble in housing prices by keeping interest rates too low for too long and for failing to rein in the explosive growth of risky and another fraudulent mortgage lending.
"Leverage is a disaster for markets -- and we try to avoid it, but we fail every time," said Greenspan, who clarified that a crisis can be triggered by an asset that is toxic.
"There are always toxic assets, you just never know, which ones are viable. Right now... it's hard to tell what the toxic asset is."
Trump, a close market-watcher who has staked his presidency on the state of the economy, has accused Powell of trying to undercut him politically by slowing the economy down.
He blamed the Fed for the market rout in October, calling the Fed "out of control" and suggesting Powell seemed to enjoy raising rates. He also later called the Fed a "much bigger problem than China," referring to a trade war between the two countries.
Before markets opened on Tuesday, Trump tweeted yet another fresh warning to Fed officials to slow down their rate hike plans, while encouraging policymakers to read a Wall Street Journal editorial "before they make another mistake."
Greenspan, however, dismissed the idea that the Fed might cave to political pressure by President Trump.
"I've seen no evidence of that," said Greenspan, who said during his tenure he figuratively wore "ear muffs myself." He also said he never recalled a time when someone had wished he had raised rates.
"We listen — sometimes respectfully, sometimes not," he said. "But do we change policy? 'No.'"
Greenspan also said that the stock market does not see equity prices going any higher than they are now.
"It would be very surprising to see it sort of stabilize here, and then take off," he said.
He added that markets could still go up further — but warned investors that the correction would be painful: "At the end of that run, run for cover." PTI AKJ AKJ
(With inputs from agencies.)