CHICAGO, Sept 8 (Reuters) - U.S. wheat futures fell on Wednesday, dragged lower by a firmer dollar that threatened to make U.S. supplies less competitive on the export market, traders said.

Corn futures steadied after sinking to their lowest in two months early in the day, with bearish harvest expectations limiting any rally attempts.

The soybean market was slightly higher after falling for six of the previous eight sessions.

Traders noted position-squaring in corn and soybeans ahead of the U.S. Agriculture Department's monthly World Agricultural Supply and Demand Estimates report on Friday.

"The market has pretty much convinced itself that the USDA will publish larger U.S. corn crop estimates," said Tobin Gorey, director of agricultural strategy at Commonwealth Bank of Australia.

At 12:04 p.m. CDT (1704 GMT), Chicago Board of Trade December corn futures were flat at $5.10-3/4 a bushel.

In a weekly update on Tuesday afternoon, the USDA estimated 59% of the U.S. corn crop to be in good-to-excellent condition, down 1 percentage point. Analysts surveyed by Reuters on average had expected no change.

CBOT November soybeans were 1 cent higher at $12.78 a bushel.

CBOT December soft red winter wheat shed 9-1/4 cents to $7.10-1/2 a bushel. MGEX December spring wheat notched the biggest losses in the wheat complex, dropping 13-3/4 cents to $8.94-1/2 a bushel.

Spring wheat faced additional pressure as farmers neared the end of harvest in the northern U.S. Plains earlier than usual. USDA said 95% of the crop had been harvested, up from 80% in early September 2020 and ahead of the five-year average of 83%.

Egypt's state grains buyer said on Wednesday that it bought 300,000 tonnes of wheat to be sourced from Russia and Ukraine in an international tender. There were no offers for U.S. wheat in the tender. (Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Sherry Jacob-Phillips, David Evans and Mark Heinrich)