BEIJING, Oct 30 (Reuters) - Shanghai base metal prices fell on Tuesday after a report that the United States is planning potential tariffs on an additional $257 billion of Chinese goods. Prices have been weighed down by tit-for-tat tariffs imposed by the world's top two economies this year amid concerns the trade row will hurt demand for industrial metals. "Falling inventories and rising premiums continue to indicate the fundamentals remain positive for ... metals," ANZ wrote in a note. "However, rumours of more U.S. tariffs on Chinese goods triggered a sell-off." Any signs of weakening global economic growth from data out this week "would see commodity markets come under further pressure", the bank added. FUNDAMENTALS * LME COPPER: Three-month copper on the London Metal Exchange had slipped 0.2 percent to $6,145 a tonne by 0338 GMT, having ended the previous session flat with support from tumbling inventories. * COPPER PREMIUMS: The premium for the cash over the three-month LME copper contract CMCU0-3 was last at $18.50 a tonne, having hit a three-year high of $47 a tonne on Friday in a sign of immediate market tightness. * SHFE COPPER: The most-traded December copper contract on the Shanghai Futures Exchange had fallen by 0.2 percent to 49,780 yuan ($7,144.09) a tonne by the end of the morning session. * OTHER METALS: Zinc was hit hardest, dropping as much as 1.6 percent in London to a two-week low of $2,580.5 a tonne. The metal used to galvanise steel also fell as much as 2.4 percent in Shanghai to 21,675 yuan a tonne, the weakest since Oct. 9, as China's ferrous complex also moved lower. * BHP: The world's biggest miner BHP Billiton has trimmed its expectations of global growth for next year and 2020 due to a "lose-lose" result from the U.S.-China trade conflict, a senior executive said on Tuesday.