President Donald Trump delivers a speech during a special address on the opening day of the World Economic Forum (WEF) in Davos, Switzerland, on Tuesday, Jan. 21, 2020.

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 Chinese trade officials have privately told business leaders they hope all tariffs will be removed before a new trade deal. 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. first slapped on China 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 an agreement can be reached.

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, president of political consulting firm Eurasia Group, 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 much as it promised.