* Traders eye next week's USDA monthly supply-demand report

* Drop in Australia's crop forecast was 'friendly' -broker

* Exchange stocks hold steady at 7-month highs

NEW YORK, March 4 (Reuters) - Cotton futures gained for a second straight session on Tuesday, lifted by chart signals and expectations of tight supplies in the United States, the world's top exporter.

The most-active May cotton contract on ICE Futures U.S. rose 0.89 cent, or 1 percent, to settle at 89.22 cents a lb.

"There's a bullish tug on the market as we exhaust last year's supplies," said Keith Brown, cotton broker at Keith Brown & Co in Moultrie, Georgia, who also pointed to a strong technical outlook.

Dealers eyed the U.S. Agriculture Department's monthly supply-demand report due on Monday. The report is widely expected to show a reduced outlook for U.S. inventories by the end of July.

The second-month contract touched a six-month high of 90.44 cents a lb last week.

Weekly U.S. government data last week showed that recent high prices have crimped U.S. export demand, but mill fixations continued to underpin the market, traders said.

A lowered forecast for cotton output in Australia released after Monday's close was also "friendly" to prices, Brown said.

Australian cotton production is projected to fall 11.4 percent to 833,000 tonnes in the 2014/15 crop year as farmers abandon dryland acres.

The market continued to digest rumors that Beijing will cut its selling price for bales in a bid to boost buying of domestic fiber and whittle down ballooning state reserves.

The sales are expected to be linked to import quotas and to support demand for foreign fiber.

ICE inventories held steady on Monday at 259,095 bales, the highest level since July 2013, according to the most recent exchange data compiled by Reuters. (Reporting by Chris Prentice; Editing by Peter Galloway)