* Wheat firms after dropping on Monday 3.5% to nearly 3-week low * Australian forecast of 10% more output to keep lid on prices (Adds details on Australian wheat crop, quotes) SINGAPORE, Dec 1 (Reuters) - Chicago wheat futures edged higher on Tuesday on bargain buying following previous session’s deep losses, although forecasts of a near record Australian crop and higher Russian exports curbed gains. Corn and soybeans rose marginally in Asian trade after closing lower on Monday. Australian farmers are forecast to harvest more than 30 million tonnes of wheat this season, after the country’s production estimate was raised by nearly 10% due to favourable rainfalls. The Australian Bureau of Agricultural and Resource Economics and Sciences (ABARES) said wheat production during the 2020/21 season would total 31.17 million tonnes, up from a September estimate of 28.91 million tonnes and not far off an all-time high of 31.8 million tonnes in 2016/17. “Australian crop keeps getting bigger and ABARES needs to add another 2 million tonnes to their estimate,” said Ole Houe, director of advisory services at agriculture brokerage IKON Commodities in Sydney. “In last big crop year, ABARES increased total winter crop by 4 million tonnes from December to February update.” The most-active wheat contract on the Chicago Board Of Trade (CBOT) added 0.4% to $5.87-1/4 a bushel by 0347 GMT, after sliding more than 3% on Monday. Corn rose 0.5% to $4.28 a bushel and soybeans gained 0.3% at $11.72-1/4 a bushel. Wheat fell on Monday after Russia’s Agriculture Ministry said the country may increase the size of its grain export quota planned for Feb. 15 to June 30 to 17.5 million tonnes, from 15 million tonnes. Sovecon agriculture consultancy said on Monday it expected Russia to harvest 79.2-82.8 million tonnes of wheat in 2021, compared with 85.3 million tonnes in 2020. Egypt’s main state wheat buyer set an international wheat purchase tender on Monday after CBOT close, its second within a week. Results are expected on Tuesday. Large speculators raised their net long position in CBOT corn futures in the week to Nov. 24, data released on Monday showed. The Commodity Futures Trading Commission’s weekly commitments of traders report also showed that non-commercial traders, a category that includes hedge funds, trimmed their net short position in CBOT wheat and cut their net long position in soybeans. U.S. soybean crushings in October likely reached a record-high 5.899 million short tons, or 196.6 million bushels, according to the average forecast of nine analysts surveyed by Reuters ahead of a monthly U.S. Department of Agriculture (USDA) report. The USDA is scheduled to release its monthly fats and oils report later in the day. (Reporting by Naveen Thukral, Editing by Sherry Jacob-Phillips and Rashmi Aich)