Benchmarks in London and Frankfurt advanced after Shanghai and Tokyo closed lower, while Wall Street was poised for gains at the market open.
China's foreign ministry has expressed hope that the U.S. government can "meet China halfway" amid a costly tariff fight over trade and technology.
Investors are hoping for a repeat of Trump and Xi's December agreement to postpone new tariff hikes while they negotiated over trade and technology. But analysts caution any new truce at the Group of 20 meeting of major economies is likely to be temporary because negotiators face the same disagreements that caused talks to break down in May.
"We have watched this movie before: China and the U.S. talk, leaks from policymakers on both sides encourage speculation we are close to a deal, things fall apart," said Hannah Anderson of J.P. Morgan Asset Management in a report.
In midday trading, Frankfurt's DAX added 0.5% to 12,334. London's FTSE 100 advanced 0.2% percent to 7,415 and France's CAC 40 also gained 0.3% to 5,510.
On Wall Street, the future for the benchmark Standard & Poor's 500 index was up 0.2% percent as was the Dow Jones Industrial Average.
The Shanghai Composite Index lost 0.6% to 2,978.88 and Tokyo's Nikkei 225 retreated 0.3% to 21,275.92. Hong Kong's Hang Seng shed 0.3% to 28,546.74.
Seoul's Kospi was 0.2% lower at 2,130.62 and Sydney's S&P-ASX 200 lost 0.7% to 6,618.80. India's Sensex was 0.1% lower at 39,562.22. New Zealand and Singapore gained while Taiwan and the Philippines retreated.
This weekend marks the first face-to-face meeting between Trump and Xi since the American president said he was preparing to target the $300 billion in Chinese imports that he hasn't already hit with tariffs, extending them to everything China ships to the United States.
The two sides are in a stalemate after 11 rounds of talks that failed to overcome U.S. concerns over China's acquisition of American technology and its massive trade surplus. China denies forcing U.S. companies to hand over trade secrets and says the surplus is much smaller than it appears once the trade in services and the value extracted by U.S. companies are taken into account.
Despite worries over trade, investors have mostly pushed stocks higher this month as the Federal Reserve raised expectations that it is prepared to cut interest rates if needed to shield the economy should the damage from the costly trade conflict worsen.
ENERGY: Benchmark U.S. gained 5 cents to $59.48 per barrel in electronic trading on the New York Mercantile Exchange. The contract gained 5 cents on Thursday to close at $59.43. Brent crude, used to price international oils, gained 5 cents to $65.72. The contract lost 2 cents the previous session to $65.67.
CURRENCY: The dollar declined to 107.72 yen from Thursday's 107.79 yen. The euro gained to $1.1377 from $1.1371.