Executives at three top Japanese companies said officials had been in touch asking for investment numbers. Public investment institutions say the prime minister is also leaning on them to pledge tens of billions of dollars to U.S. infrastructure projects such as high-speed rail.
Mr Abe's extraordinary effort to bring gifts highlights his determination to forge a personal bond with the US president. He aims to gain influence over U.S. policy in Asia and head off tensions about trade or the cost of maintaining U.S. forces in Japan.
Mr Abe will arrive in the U.S. on Friday, accompanied by his finance, foreign and trade ministers. After a summit in Washington, he will spend Saturday playing golf with Mr Trump at the president's Mar-a-Lago resort in Florida.
"The most important thing is to reconfirm the importance of the US-Japan relationship in politics, economics and security," said Sadayuki Sakakibara, chairman of Japan's Keidanren business federation.
Given friction over trade and the yen, Mr Sakakibara urged Mr Abe to tell the president about the $400bn of direct investment and 1.7m jobs that he says Japanese companies support in the U.S. "We're contributing to the expansion of US exports and want to let him know that," he said.
The prime minister met Akio Toyoda, Toyota chief executive, last week to discuss Japan's car exports and U.S. manufacturing, after Mr Trump singled out the auto group for criticism over its plans for a new plant in Mexico.
Following the criticism, Toyota in January pledged to invest $10 billion in the U.S. over the next five years, including proposals to add 400 jobs at its plant in Princeton, Indiana.
Mr Trump in December welcomed a pledge by SoftBank, the Japanese technology conglomerate, to invest $50 billion in the U.S. over the next four years as part of the new tech mega-fund it is raising.
The U.S. president has also implied that Japan manipulates the value of the yen — a suggestion Mr Abe vehemently rejects.
Given that Mr Abe is only pulling together existing investment plans, some companies fear that rather than mollify the president, any pledge could become a baseline Japan has to exceed.
"Just because Donald Trump has been elected doesn't mean we immediately change our business plan," said one senior executive at a large Japanese manufacturer. "We can only invest in factories we actually need."
The second plank of Mr Abe's draft "U.S.-Japan growth and employment initiative" is the proposal for Japanese public investors to put money behind Mr Trump's plan for an infrastructure stimulus financed by tax credits.
Japanese support could take the form of export credits, loans from the Japan Bank for International Co-operation or purchases of infrastructure bonds via Japan's foreign exchange reserves. Although independent, the huge Government Pension Investment Fund has plans to invest in global infrastructure and could also be wrapped into any figure Mr Abe presents.
The prime minister is likely to push Japan's shinkansen high-speed rail technology for routes such as Dallas-Houston and Los Angeles-San Francisco. His repeated efforts to interest Barack Obama, the former president, in the shinkansen enjoyed little success. Gulf of Mexico ports are another potential target for investment.
One banker said he was concerned Mr Abe would make big pledges without addressing the obstacles. Infrastructure bond investors were concerned about US withholding taxes, the banker said.
"Buy American" rules on public investment are a further hurdle for efforts to export the shinkansen, but they will be hard for Mr Abe to raise given Mr Trump's focus on tougher trade restrictions and boosting manufacturing in the U.S.