The leaders may publicly voice support for the multi-billion-dollar Texas project after Wednesday's talks, which have been partly overshadowed by U.S. opposition to another Japanese investment, Nippon Steel's planned purchase of U.S. Steel.
Prime Minister Fumio Kishida's state visit to Washington, the first by a Japanese leader in nine years, aims to showcase closer security and economic ties between the allies.
The project linking Dallas and Houston will be on the agenda for the talks, said three sources familiar with summit preparations, who sought anonymity as they were not allowed to speak to the media.
It is likely to be mentioned in joint statements following the talks, two of the sources said.
However, a senior Biden administration official said the project did not appear to have matured to the point where the leaders would announce progress publicly.
All the sources cautioned that the details of the final agreements could change before the visit.
Japan's foreign ministry declined to comment, saying the governments were still coordinating joint statements from the talks. The White House declined to comment.
Support from the leaders could unlock new cash from the Federal Railroad Administration and other Department of Transportation funds.
But the project, estimated to cost between $25 billion and $30 billion, still faces potential hurdles in Texas and the U.S. Congress.
Biden's Transportation Secretary Pete Buttigieg has voiced support for the plan.
"We believe in this," he said in an interview with NBC 5 on Sunday. "Obviously it has to turn into a more specific design and vision but everything I've seen makes me very excited."
With its vast distances between major cities, huge commuter population, and dearth of public transport the United States has attracted multiple high-speed rail proposals.
But none have ever been built, blocked by political wrangling, land ownership riddles and skyrocketing costs.
A train linking Houston and Dallas, the U.S.'s fourth and fifth biggest metropolitan areas by population, has been discussed since the 1980s. Previous efforts were stymied by the objections of private landowners along its route.
Biden and Kishida's support, say the project's advocates, will help attract money from private investors for a "shovel ready" plan.
The 240-mile (380-km)-long rail link, which will be built and operated by Texas Central Partners and Amtrak, is expected to cut travel times between the cities to about 90 minutes, from 3-1/2 hours by car.
Japanese state lenders, including the Japan Bank for International Corporation, have provided loans to help develop the project, which is procuring shinkansen bullet train technology from Central Japan Railways Company.
Progress with the project would be a win for the Biden administration, which has pushed climate-friendly policies and rail investment.
But it is likely to draw criticism, particularly from hardline Republican lawmakers in the U.S. House of Representatives who have opposed using public funds for rail projects in the past, and oppose using them now to rebuild Baltimore' Francis Scott Key Bridge, which was destroyed by a cargo ship last month.
Plans for a possible nod of support from leaders follow Biden's opposition to Nippon Steel's plan to buy U.S. Steel Corp, saying it must remain in U.S. hands.
Biden, who signed a $1-trillion infrastructure bill in 2021 that includes $66 billion for rail projects, will face Donald Trump in November's presidential election rematch.
With voters rating the economy at the top of their concerns, Democratic president Biden has pushed government-backed building projects that his aides argue could create jobs and relieve inflation pressures.
