* Reserve sales pick up in China after price cuts

* July/Dec spread narrows for 3rd straight session

* Index fund roll pressures nearby contract prices

NEW YORK, April 2 (Reuters) - ICE cotton fell for a third straight day and looked to be headed for its first weekly loss in five weeks under pressure from market spreads and worries that supplies in the United States, the world's top exporter, will increase as demand wanes.

The most active May cotton contract on ICE Futures U.S. eased 0.56 cent, or 0.6 percent, to settle at 91.51 cents a lb.

Prices remained under pressure from expectations that U.S. farmers plan to boost cotton acreage this year after cotton prices rallied in 2013.

The U.S. Agriculture Department said this week that farmers are set to boost plantings 7 percent from the previous year.

Nearby contracts were particularly pressured as traders rolled positions forward.

"The fund roll has started," said Jobe Moss, a broker at MCM Inc in Lubbock, Texas. "These high prices are destroying demand."

The boost in acres in the world's top exporter is expected to coincide with a sharp cut in import demand from top consumer China as Beijing readies an overhaul of its stockpiling program.

Traders were waiting for U.S. government weekly export data due on Thursday, looking for any signs that a price runup last week to two-year highs above 97 cents a lb hurt demand.

Further, reserve sales in top consumer China have picked up after China cut prices in a bid to whittle down its huge stocks.

The spread between the second-month July contract, which represents the current crop, and the December contract , which represents the 14/15 crop, narrowed for a third straight session.

It ticked down to 12.26 cents a lb from 12.63 cents a lb previously, and down from 13.68 cents a lb on Friday, the highest such premium since June 2011. (Reporting by Chris Prentice; Editing by Peter Galloway)