Donald Trump delivers a speech at the Congres center during the World Economic Forum (WEF) annual meeting in Davos, on January 21, 2020.

Fabrice Coffrini | AFP | Getty Images

DAVOS, Switzerland – Many business leaders at the World Economic Forum aren’t convinced the latest round of trade negotiations between China and the U.S. will yield a “phase two” deal before the end of President Donald Trump’s first term.

The biggest potential stumbling blocks: U.S. tariffs on Chinese goods and Chinese pledges to buy more American products.

One executive who is close to Trump said that business leaders have heard from Chinese trade officials who are privately acknowledging that they hope for all of the tariffs to be removed by the time the next trade deal is signed. This executive declined to be named since the conversations were deemed private.

A phase two deal is expected to lead to a rollback of billions of dollars of tariffs that the U.S. hit were first laid onto China by the U.S. in 2018. Trump has said he may want to wait until after the election to sign a phase two trade deal and there hasn’t been a clear timeline from the White House as to when they expect the two sides to come to an agreement.

Treasury Secretary Steven Mnuchin, who is in Davos with the president, told The Wall Street Journal the next agreement could remove some but not all of the tariffs.

Doubts about a second deal were likely to dominate conversations at the elite gathering in the Swiss Alps, particularly as business leaders talk with White House officials there and in the coming months as Trump pursues his reelection. It is unclear how another China trade deal could be accomplished if Trump isn’t reelected. More than a dozen Democrats are vying for their party’s nomination to take on Trump in November, including former Vice President Joe Biden, Sens. Bernie Sanders and Elizabeth Warren, and former mayors Pete Buttigieg and Mike Bloomberg.

“No one thinks it’s going to happen,” Ian Bremmer, the president of Eurasia Group, a political consulting firm, told CNBC after being asked where Davos attendees stand on future trade talks. “I really would be shocked to see a trade two deal get done before the election.” He noted one of the hurdles to another agreement could come down to China not buying as many goods as they promised.

A White House spokesperson did not return a request for comment.

The phase one deal demands that China increase their purchases of U.S. manufacturing, energy and agricultural goods and services by at least $200 billion over two years. It also includes provisions to root out intellectual property theft and forced technology transfers.

During his speech Tuesday in Davos, Trump reaffirmed that tariffs on China will remain in place and noted that these trade barriers have been a key negotiating tool.

“These achievements would not have been possible without the implementation of tariffs, which we had to use. And we’re using them on others, too,” Trump said. “That is why most of our tariffs on China will remain in place during the ‘phase two’ negotiations.”

Michael Corbat, the CEO of Citigroup, said he believes that the remaining tariffs on China will keep them at the negotiating table. But he noted that Trump is going to be under pressure by corporate CEOs and congressional leaders to get a phase two deal done if he gets reelected.

“I don’t think we see phase two in the remainder of this term, but I think if he is reelected certain people are going to try to hold his feet to the fire to deliver on this. I think some Democrats are going to come back and say, ‘You promised us this and you haven’t done it,'” Corbat said on the sidelines of Davos.

Citigroup does business all over the world, including extensive work in China.

Ray Dalio, who leads investment firm Bridgewater Associates, said he, too, doesn’t see a phase two deal getting done by the end of Trump’s first term. Yet Dalio also suggested that he wasn’t convinced phase one wasn’t as big of an accomplishment in the broader context of ongoing trade disputes between the two nations.

“I think it’s such a tiny thing as it almost doesn’t matter, in the whole scope of the issues. There are big issues,” Dalio told CNBC outside the conference center.

Finally, Richard Trumka, the president of the AFL-CIO and a supporter of Trump’s updated North American trade deal, poured some additional cold water on phase two hopes. The labor leader told CNBC that he does not believe phase two is a priority for the Trump administration.