Asian shares extended gains on Monday to hit a three-month high as risk assets got a fillip from hopes of a U.S.-China trade deal as soon as next month while the dollar marked time as focus shifts to a U.S. rate decision.

In early Asian trades, MSCI's broadest index of Asia-Pacific shares outside Japan added 0.3 percent for its third straight day of gains to 518.29, the highest since late July.

Chinese shares were a tad firmer with the blue-chip CSI 300 up 0.2 percent. Hong Kong's Hang Seng Index jumped 0.7 percent while Australian shares climbed 0.1 percent.

Japan's Nikkei was also upbeat, rising 0.3 percent to a decade high.

The gains came after a positive session in the U.S. and European markets on Friday.

The U.S. and Chinese officials have basically completed some parts of a trade agreement after high-level telephonic discussions on Friday, China's Commerce Ministry and the U.S. Trade Representative's office said, with talks to continue.

Optimism that Beijing and Washington were finally close to resolving their dispute led the S&P 500 to surpass its July 26 closing record of 3,025.86, though it ended a tad below that level on Friday. The S&P 500's total return index posted an all-time high.

E-mini futures for the S&P 500 started firm on Monday, up 0.1 percent.

Activity later in the week will be dominated by the U.S. Federal Reserve, which markets expect is all but certain to lower interest rates at its Wednesday meeting.