* U.S. and China presidents in contact over potential deal * U.S. jobs growth improves oil demand outlook * Fed interest rate cut, weakened dollar supports oil (Updates with settlement prices, adds Cushing oil stocks estimate) HOUSTON, Nov 4 (Reuters) – Oil prices rose on Monday, buoyed by an improved outlook for crude demand as better-than-expected U.S. jobs growth added to market hopes a preliminary U.S.-China trade deal would be reached this month. Brent crude futures for January settled at $62.13 a barrel, up 44 cents, or 0.7%. December U.S. crude futures rose 34 cents, or 0.6%, to end at $56.54 a barrel. Market optimism about progress in U.S.-China trade negotiations propelled U.S. stock indexes to record highs on Monday, elevating oil. Energy shares gained the most of the 11 major S&P 500 sectors. Chinese President Xi Jinping and U.S. President Donald Trump have been in continuous touch through “various means,” China said on Monday, when asked when and where the two leaders might meet to sign a trade deal. “Both sides (China and the United States) are talking up the trade deal to a large degree. And you have the Federal Reserve leaning into this better-looking economic situation, […]