Sanae Takaichi’s bid to be elected as Japan’s first female Prime Minister appeared to gain some momentum this week, with a key parliamentary vote to pick the next premier scheduled for Tuesday.

Takaichi, the leader of the Liberal Democratic Party, has been holding negotiations with the right-leading Japan Innovation Party -- or Ishin -- following the collapse of a more than two-decade old partnership with the Komeito Party earlier this month.

On Friday, party executives said "big progress" had been made in talks towards clinching a potential coalition, Reuters reported.

The LDP and Ishin together hold a combined 231 seats in the lower house of Japan’s parliament, just two shy of the simple majority needed for Takaichi to win the premiership. To get those remaining votes, the LDP has been asking for cooperation from smaller parties.

Media reports said Ishin has also decided to pull out of talks with the smaller Constitutional Democratic Party and Democratic Party for the People over forming a three-way coalition to rival the LDP -- which has ruled Japan for nearly all of its post-war history.

However, some issues still need to reportedly be ironed out between the LDP and Ishin before a final decision on their partnership is made, Reuters reported. Notably, it is unclear if Ishin will join the LDP in a formal coalition or it will only lend its political backing.

In a note to clients, analysts at Deutsche Bank said the priority for both parties will be to simultaneous prevent defections from Ishin and attract independent lawmakers. Should they end up securing a simple majority in the lower house, the stability of the new premier’s administration would significantly increase," they added.

For financial markets, Takaichi is seen as far more fiscally dovish than predecessor Shigeru Ishiba, and has supported tax cuts and accommodative policy for the Japanese economy.

Takaichi has in the past opposed interest rate hikes by the Bank of Japan, and is widely expected to maintain this stance as Prime Minister. More fiscal spending, with Takaichi having outlined plans for tax breaks, subsidies, and consumer support, is also anticipated to further boost Japanese economic growth and corporate earnings.

"[I]f the LDP and Ishin form a coalition and Takaichi is selected as prime minister, the likelihood of an aggressive fiscal policy, including a consumption tax rate reduction, would be higher than under a sole LDP administration," the Deutsche Bank analysts said.