He cautioned against meddling with home prices or interest rates to address the housing problem.
Greenspan did not specifically call for a tax cut. Instead, he called for the government to apply money to the severe housing market slump. Such a cash infusion would typically come through a tax break or a new government spending program.
"Cash is available and we should use that in larger amounts, as is necessary, to solve the problems of the stress of this," Greenspan said during an appearance on ABC's "This Week."
Separately, Greenspan said he is concerned about signs of a resurgence of inflation.
"Core inflation is up. Wholesale prices had their highest increase I think in a generation. That raises the specter of stagflation again," said Greenspan, referring to a simultaneous stagnant economy and upward pressure on prices.
He said the Federal Reserve should "do what it has to do to suppress the inflation rates that I see emerging, not immediately, but clearly over the intermediate and longer term period."
Greenspan said a large number of people are in major financial stress, even when they've tried exceptionally hard to make their monthly mortgage payment. But some political solutions would only prolong their agony, he said.
"It's far less damaging to the economy to create a short-term fiscal problem, which we would, than to try to fix the prices of homes or interest rates. If you do that, it'll drag this process out indefinitely," said Greenspan, referring to his preference for a cash infusion to help homeowners.
Greenspan ran the central bank for more than 18 years. He has been criticized by some for keeping interest rates too low for too long after the 2001 recession.
He said - as he did earlier in the week in another interview - that he agrees with some experts who see prospects for a recession at about 50-50.
"Whether it's above or below [50 percent] is really extraordinarily difficult to tell," Greenspan said.Greenspan said the key lesson the economy has provided lawmakers over the last 20 years is that inflation must be suppressed for sustained economic growth to occur.