"Looks like we will be signing something in (the) next couple of days and over agriculture and produce," Trump spokeswoman Stephanie Grisham said on Fox Business.
Trump and Abe are in New York for the annual meeting of the UN General Assembly and they are due to meet on Wednesday.
Earlier this month, Trump said an initial agreement had been reached on tariffs.
The deal appears to focus on agricultural products, which represent a politically important sector for Trump as he pursues a difficult 2020, reelection bid.
That earlier statement also referred to an agreement on digital trade. However other heavyweight sectors, including automobiles, were not mentioned.
Trump said that a "comprehensive trade agreement" required further negotiation.
Under pressure from the deepening trade dispute with China, Trump is eager for something to show his supporters.
Farmers are a relatively small but highly symbolic part of his coalition, with an important role in electorally important states like Iowa.
Abe, an ally of Trump's, last month said the two nations had reached consensus after "intense" negotiations.