CHICAGO, Sept 29 (Reuters) - U.S. corn and soybean futures closed lower on Tuesday on expectations of rapid harvest progress this week and a slowdown in demand from China, a big buyer of U.S. soybeans and corn, in recent weeks, analysts said.

Wheat futures also fell but declines in all three commodities were muted as traders squared positions ahead of quarterly stocks data due on Wednesday from the U.S. Department of Agriculture.

Chicago Board of Trade December corn settled down 2 cents at $3.64-3/4 per bushel. November soybeans ended down 3-1/4 cents at $9.93 a bushel and December wheat finished down 3/4 cent at $5.49-1/2 a bushel.

Weather forecasts called for mostly dry conditions over the next week in the U.S. Corn Belt, which should favor field work.

"We could be seeing rapid harvest progress pretty much across the Corn Belt. We look for a big jump in harvesting numbers next week," said Terry Reilly, senior analyst with Futures International in Chicago.

The USDA said late Monday the U.S. corn crop was 15% harvested, behind the five-year average of 16%, while soybeans were 20% harvested, ahead of the five-year average of 15%.

On the export front, the USDA confirmed private sales of 100,000 tonnes of U.S. soybeans to Mexico, but the agency has not announced any fresh soybean sales to top global buyer China since Sept. 23.

"U.S. export developments are a little quieter this week, so that is another reason for the downward pressure," Reilly said.

The USDA on Wednesday is scheduled to report on the amount of U.S. grain and soy stored on and off farms as of Sept. 1, a quarterly report that has a history of jolting CBOT futures markets.

The USDA on Wednesday will also update its estimates of U.S. 2020 wheat production. (Reporting by Julie Ingwersen; Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; editing by Uttaresh.V, Mark Potter and Grant McCool)