The government has said it will decide its nominee this week and Abe was expected to huddle with aides to reach a final decision after returning from a U.S. trip on Sunday.
Still, whoever Abe nominates is not certain to get the job because the appointment must be approved by both houses of parliament.
Abe's ruling bloc does not have a majority in the upper house, and as a result the government will consult opposition parties before naming its choices for the Bank of Japan's (BOJ)top posts - the governor and two deputy governors - when incumbents retire on March 19.
Former top financial bureaucrat Toshiro Muto had been considered the leading candidate to replace Masaaki Shirakawa, who leaves after a five-year term. Muto remains on the shortlist, strongly backed by officials at the Ministry of Finance.
But evidence is building that the race between Muto, ADB President Haruhiko Kuroda and former BOJ deputy governor Kazumasa Iwata may be closer than thought, say officials and lawmakers familiar with the selection process.
Abe, who won a resounding election victory in December promising to finally rid Japan of nearly 20 years of deflation, wants a fresh face in the job, someone keener to experiment with radical measures, the sources said.
"Muto is preferred by finance ministry bureaucrats, while people close to Abe want someone else," said one of the sources, who spoke on condition of anonymity due to the sensitivity of the matter.
"How markets may react is also important," the source said, adding Abe may want to avoid disappointing markets already pricing in a radical makeover of monetary policy under a new BOJ leadership. His policy prescription, dubbed "Abenomics", has pushed the yen to its lowest level in more than three years.
Tokyo share prices fell briefly after Reuters reported on February 15 that Muto was leading the BOJ race, as investors saw him as a policymaker who would be more aggressive with policy than the outgoing Shirakawa, but who would refrain from the more unorthodox steps advocated by some candidates.
"The choice will have a huge impact on the current market trend of yen weakness and share price gains," top government spokesman Yoshihide Suga told a television program on Sunday.
"It will be made based mainly on whether the person will pursue the bold monetary policy that the premier is seeking," he said, suggesting that a candidate with reflationary views like Kuroda may be favored over moderates like Muto.
Abe has the power to choose the government's nominee for BOJ governor, although the premier usually respects the views of the finance minister and the ministry's bureaucrats because they work closely with the central bank in economic policymaking.
The finance ministry wields a great deal of influence over monetary policy and personnel decisions.
Still, Finance Minister Taro Aso told reporters on Friday the new BOJ governor does not necessarily have to be someone from his ministry, leaving room to support candidates besides Muto if Abe insists on someone more radical.
Abe hardened his comments last week on the need for a new governor to have international contacts as a key qualification for the post, suggesting that he prefers someone with experience in financial diplomacy. Muto spent most of his career in domestic affairs, climbing the career ladder at the ministry of finance to become its top bureaucrat.
"Japan now needs a governor who can join, communicate and convince people in the inner circles of global finance," Abe told parliament on Wednesday.
That would put the ADB's Kuroda, who was Japan's top currency diplomat in the midst of the Asian financial crisis in the late 1990s, at the top of the list. As president of the 67-member ADB, which includes countries outside Asia, he rubs shoulders with policymakers the world over.
Several Japanese media - including the Asahi newspaper and Kyodo and Jiji news agencies - said at the weekend that Abe had firmed up his decision to nominate Kuroda.
Indeed, Kuroda meets many other qualifications suggested by Abe's cabinet ministers and opposition parties, such as experience managing a large organization, strong English skills, and sharing Abe's calls for bolder monetary stimulus.
Kazumasa Iwata, a former deputy BOJ governor, also remains a strong candidate as a result of his fluent English, renowned academic work on economic policy, and his consistent calls for more aggressive bond buying by the central bank.
Both of them face hurdles to selection. Kuroda would have to quit his job at the ADB, which could weaken Japan's standing as the country that traditionally provides the head of that organization.
Should Iwata get the top job, his repeated calls for the BOJ to create a fund to buy foreign bonds could raise suspicions among Japan's Group of Seven peers that Tokyo is targeting the yen with monetary policy.
More radical candidates from academia like Kikuo Iwata and Takatoshi Ito, while favored by Abe and his aides, may have slimmer chances because they lack managerial experience, the sources said.
The selection process for the top BOJ posts will start in earnest now Abe has returned from Washington.
Delicate political maneuvering is still needed to ensure parliamentary approval.
The prime minister is keen to avoid a rerun of the debacle in 2008 when the seat for the BOJ chief was vacant for weeks because the main opposition Democratic Party of Japan (DPJ) blocked the nomination of Muto and other former finance officials, arguing they might erode central bank independence.
Muto's chances could improve if Abe can win support from the DPJ, which has signaled it would not rule out ex-bureaucrats this time, while saying radical proponents of reflation were not desirable.
Other candidates will have a better chance if Abe is forced to rely on support from fringe parties like Your Party, which is opposed to ex-bureaucrats and wants the governor to be a fluent English speaker, which Muto is not.
(Additional reporting by Sumio Ito, Yoshifumi Takemoto, Shinji Kitamura, Yuko Yoshikawa and Linda Sieg; Editing by Neil Fullick and Daniel Magnowski)
By Leika Kihara