A rally in stocks is likely to follow the recent battering shares took globally because of fears of a U.S. recession, but such a rally would be short-lived, Jim Rogers, CEO of Roger Holdings, told "Squawk Box Europe."

Hopes that the Federal Reserve will cut rates by a further 50 basis points this week after last week's surprise 75 basis points cut lifted Asian and European stocks Tuesday, but Rogers said there should be no further monetary policy easing.