The banking expert made the comments during an appearance on NBC’s Meet the Press program.
He said: “It's important to remember that equity values, stock prices, are not just paper profits. They actually have a profoundly important impact on economic activity."
If stock prices were to continue falling, then he would be "very concerned”, the banker explained.
Mr Greenspan made the statement following the fourth consecutive weekly decline in stock prices – the longest run of falls in share values since July of last year.
He added that it is unlikely the current levels of unemployment will drop, instead predicting that they will remain at approximately nine per cent for most of 2010.
“It’s very difficult to make the case that unemployment is coming down any time soon,” he said during the interview.
The finance expert was chairman of the Fed between 1987 and 2006.
By Jim Ottewill