Sanae Takaichi, leader of the conservative LDP, and Hirofumi Yoshimura, head of the smaller right-leaning group known as Ishin, are set to sign an agreement on their alliance on Monday, Kyodo news agency reported on Sunday.
Ishin's co-head, Fumitake Fujita, raised expectations for a deal on Friday, saying the two parties had made "big progress" in coalition talks.
Ishin lawmakers will vote for Takaichi in an election to choose the prime minister in parliament on Tuesday, but the party does not plan to send ministers to Takaichi's cabinet initially, the news agency said.
That would fall short of the full-fledged alliance the LDP maintained with the Komeito party until the junior partner quit the coalition in October, raising concern over the stability of the forthcoming government.
Takaichi's path to succeed Prime Minister Shigeru Ishiba had seemed all but certain after she won her party's presidency early in October.
But then the long-ruling LDP's junior partner, Komeito, quit their 26-year coalition, setting off a flurry of negotiations with rival parties to select the next premier.
In an effort to get Ishin on board, the LDP offered to keep working towards banning donations from companies and other organisations and exempting food items from Japan's sales tax, Kyodo said.
Ishin has proposed eliminating the tax on food items for two years.
Takaichi, a fiscal dove, has called for higher spending and tax cuts to cushion consumers from rising inflation and has criticised the Bank of Japan's decision to raise interest rates.
She favours revising Japan's pacifist postwar constitution to recognise the role of its expanding military.
Takaichi is a regular visitor to the Yasukuni shrine honouring Japan's war dead - including some executed war criminals - and is viewed by some Asian neighbours as a symbol of the nation's past militarism.
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