WASHINGTON (Reuters) - Former Federal Reserve Chairman Alan Greenspan said his successors at the U.S. central bank should be cautious about cutting interest rates because of inflation risks, and he forecast home prices will drop further, according to interviews published on Sunday. Greenspan, whose memoirs hit book shelves on Monday, said the Fed should be careful not to cut rates too aggressively because the risk of an "inflationary resurgence" is greater now than when he was chairman, the Financial Times reported. The U.S. central bank meets on Tuesday and is widely expected to cut benchmark federal funds rate -- currently at 5.25 percent -- by at least a quarter of a percent age point to help the economy weather a housing downturn and a credit crunch. Greenspan said the U.S. housing slump is likely to deepen more than many analysts expect, with home prices falling by at least a "large single-digit" percentage amount and perhaps by a double-digit percentage, he told the Financial Times. The Fed is currently weighing the adverse impacts of the housing downturn on the broader economy after a recent report showing employers shed 4,000 jobs in August raised warning flags. UNDERLYING STRENGTH SOURCE OF THIS STORY