The victor will serve out Abe's remaining term as LDP chief, which ends in September 2021.
Former defense minister Shigeru Ishiba, 63, a soft-spoken security hawk who aims to revive Japan's regional economies, is also expected to run.
A long-time Abe critic, Ishiba is popular with the public but less so among party members of parliament.
Ex-foreign minister Fumio Kishida, 63, long seen as Abe's favored heir, said on Friday he would run in the party poll, but the dovish lawmaker from Hiroshima has struggled to gain traction with voters.
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Dark-horse potential candidates include Defense Minister Taro Kono, 56, who has an image as a maverick but has toed the line on key Abe policies, and Foreign Minister Toshimitsu Motegi, 64, who has a reputation as a tough negotiator.
Environment Minister Shinjiro Koizumi is popular but at 39 seen by many as too young.
What format party executives pick to choose their next leader will have a big impact on the outcome. A decision is expected on Tuesday.
Usually, a leadership vote is held by LDP MPs along with grassroots party members.
In case of a sudden resignation, however, an extraordinary vote can be called with participants narrowed to MPs and representatives of the party's local chapters.
"A regular election gives Ishiba a better chance," said Steven Reed, professor emeritus at Chuo University.
In 2012, Ishiba beat Abe in a first-round party poll that included rank-and-file members but he failed to win a majority and lost in a run-off when only MPs voted.
Ishiba could also have an edge if LDP lawmakers put priority on a leader who would help the party keep its huge majority in a lower house election that must be held by late October 2021.
Talk of Suga as a contender bubbled up in April 2019 after he unveiled the new imperial era name, "Reiwa", for use on Japanese calendars after the enthronement of the new emperor.
Still, the veteran lawmaker has an image more as a behind-the-scenes operator than a frontline leader.
"The stamp of approval will come through dealmaking in smoky backrooms in the LDP, but whoever wins will have to prove themselves by winning the next general election," said Jesper Koll, senior adviser to asset manager Wisdom Tree Investments.
(Writer: Linda Sieg | Editors: David Dolan, William Mallard)
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