Hong Kong's Hang Seng index fell 0.52% in its final hour of trade. Chinese mainland shares were also lower: The Shanghai composite declined 0.54% to close at 3,090.04, the Shenzhen component was down 0.22% to 1,814.21 and the Shenzhen component fell 0.15% to 10,972.32.
Australia's benchmark ASX 200 bucked the downward trend and rose 0.47% to 6,994.80, with most sectors finishing up.
The session followed a muted finish on Wall Street overnight where major investment banks posted quarterly earnings.
Officials from the U.S. and China are expected to sign the trade agreement on Wednesday after the two countries last month agreed to the deal in principle, where Washington said it would cancel or reduce some tariffs in exchange for China purchasing more American products and addressing U.S. concerns on areas of technology and financial services.
The deal is expected to include a commitment from China to buy about $200 billion of U.S. goods over two years, which includes about $80 billion in manufactured goods, $53 billion in energy, $32 billion in agriculture and $35 billion in services.
"Market moves have been relatively subdued ahead of the signing," said Tapas Strickland, director of economics and markets at the National Australia Bank, in a morning note.
"Combined with news that China is no longer being pegged as a currency manipulator, this has put upward pressure on the yuan," Felicity Emmett, a senior economist at Australian bank ANZ, wrote in a morning note. "There is a sense that recent developments will bolster global growth and that downside risks to trade may have subsided somewhat."
Still, Emmett added, the scope for disappointment remains as the second phase of the U.S.-China trade deal has yet to be negotiated.
In the currency market, the U.S. dollar traded near flat at 97.335 against a basket off its peers, slipping from levels around 97.562 in the previous session.