Ahead of the trip, the White House said talks between the president and prime minister would deal with elements of the trade deal between the countries.
Despite the trade deal being agreed, a 10% tariff remains on Scotch whisky, one of the country's biggest exports.
Asked if that tariff could be dropped or eliminated as a result of the meeting with the prime minister, Trump said: "We'll talk about that, I didn't know whisky was a problem. I'm not a big whisky drinker, but maybe I should be."
The first minister said he would raise the issue when he met with the president.
A Scottish government spokesperson said the dinner on Monday would provide Swinney with an opportunity "specifically to make the case for tariff exemptions for Scotland's world class whisky and salmon sector"
On Monday, the first minister told the BBC: "Tariffs are very important for the Scottish economy and obviously Scotch whisky is a unique product.
"Obviously, the trade deal with the United States provides a degree of stability for economic connections with the United States but the application of tariffs is increasing the costs for the Scotch whisky industry.
"So one of my objectives will be to make the case to President Trump that Scotch whisky should be exempted from those tariffs," he added.
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