LONDON, Oct 5 (Reuters) - Copper prices fell on Monday as signs of weakening demand outweighed the positive mood on wider markets after reports that U.S. President Donald Trump may soon be released from hospital, where he is being treated for COVID-19.

Trump's doctors have said his health is improving and he could be discharged as soon as Monday, though the severity of his illness remains unclear.

Benchmark three-month copper on the London Metal Exchange (LME) was down 0.5% at $6,521 a tonne at 1600 GMT after tumbling to a seven-week low of $6,269 on Friday.

"Metals - and not only metals - are depending on Trump's state of health," said Commerzbank analyst Daniel Briesemann.

Copper reached $6,877.50 a tonne on Sept. 21, the highest since June 2018, after an impressive six-month rally.

But signs of slowing demand in top consumer China and rising copper stockpiles mean prices may slip lower, Briesemann said.

MARKETS: Stocks and other risk assets such as oil rose and the dollar weakened, making metals cheaper for non-U.S. buyers.

CLOSED: Chinese markets are closed until Friday for a public holiday.

CHINA: Chinese Yangshan copper import premiums have fallen to around $50 a tonne, the lowest since May 2019.

ANZ analyst Soni Kumari said there had been a shift away from a price rally linked to Chinese-led growth, "as most of the positive surprises related to China are largely priced in."

STOCKS/SPREAD: Cash copper on the LME has flipped to a discount versus the three-month contract after LME warehouse stocks more than doubled to around 160,000 tonnes last week, easing a squeeze on nearby supply.

ECONOMY: The euro zone's economic recovery faltered in September, while U.S. services industry activity accelerated above pre-coronavirus levels, PMI surveys showed.

CHILE: Chilean copper output fell 6.2% year-on-year in August to 481,700 tonnes.

BULLS: Speculative investors remain bullish with a net long position equal to 6.1% of open LME contracts as of Thursday, brokers Marex Spectron said. Speculators also hold a large net long in copper contracts on the Comex exchange.

OTHER METALS: LME aluminum was 0.6% higher at $1,778.50 a tonne, zinc fell 0.1% to $2,325.50, nickel rose 1.4% to $14,620, lead lost 0.8% to $1,757.50 and tin was up 1.4% at $18,055. (Reporting by Peter Hobson, Additional reporting by Mai Nguyen; Editing by Jan Harvey and Mark Potter)