Stock markets in Greater China posted large gains on Friday on the back of comments from U.S. President Donald Trump and a news report that both indicated potential progress in Washington's trade negotiations with Beijing.

Hong Kong's Hang Seng index surged 4.21 percent to close at 26,486.35. while the Shanghai composite gained 2.7 percent to close at around 2,676.48 and the Shenzhen composite advanced 3.428 percent to finish at 1,351.09.

Those markets, which had been higher all day, climbed higher after Bloomberg reported that Trump had asked officials in his administration to start drafting a potential trade deal with China.

Following the release of that article — which cited four unnamed sources familiar with the matter — many big-name stocks in the Hong Kong markets skyrocketed: Tencent surged 9.29 percent, ZTE jumped 12.2 percent and Geely Automobile saw gains of 11.72 percent.

The new report came amid an already buoyant day for the Greater China markets, which inherited a seemingly positive stateside development: Trump tweeted on Thursday that he had a "long and very good conversation" with Chinese President Xi Jinping in part about trade.

The president also said in his U.S. morning tweet that trade "discussions are moving along nicely" and meetings between the two leaders at the upcoming G-20 summit are being scheduled. U.S. stocks rallied in part on that signalling from the president, with all three major stock indexes seeing gains by the closing bell.

Experts have tried to read the trade "smoke signals" coming from the White House, but Rob Carnell, ING's chief economist and head of research for Asia Pacific, questioned the intention behind Trump's move. He told CNBC's "Street Signs" that the timing "feels a little bit too coincidental" given that midterm elections stateside are a few days away.

It is unclear how much progress Trump and Xi made toward breaking an impasse over how they will assuage Trump's grievances with Beijing and move toward reducing tariffs. Talks between the two countries have recently stalled as the White House pushes for an end to intellectual property theft by Chinese companies and a reduction in the U.S. trade deficit with China. Beijing has so far appeared unwilling to make major concessions.