The Israeli daily Haaretz reported on Saturday the meeting on Wednesday will be broadcast live.
Traditionally, the president selects the candidate he believes has the best chance of securing a parliamentary majority, rather than automatically nominating the leader of the largest party.
That would be incumbent Prime Minister Benjamin Netanyahu, whose right-wing Likud party emerged as the strongest force from Tuesday's parliamentary election with 27 of 120 seats.
Opposition candidate Gadi Eisenkot came second with his newly founded centrist party Yashar, which won 21 seats.
However, neither Netanyahu's bloc nor the opposition secured the 61 seats needed for a majority, leaving the composition of the next government uncertain.
The candidate commissioned by the president then has 28 days to form a coalition, with a possible extension of 14 days.
If this attempt fails, the president transfers the mandate for 28 days to another member of parliament. If this step also fails, at least 61 lawmakers can propose a candidate within 21 days, who then has 14 days to form a government.
If all three stages fail to produce a majority coalition, parliament dissolves automatically. In that case, new elections would follow within 90 days.
Herzog has said he wants to avoid new elections.
Around 2000 people demonstrated in Tel Aviv on Saturday for the participation of Arab parties in the next government.
The Joint List alliance and the conservative Islamic Raam party together won 19 seats, nearly doubling their result from the 2022 election.
Eisenkot once again tied possible participation in government to four conditions.
The core demands include a commitment to Israel as a Jewish, democratic and liberal state with equal legal status for all citizens and classifying Hamas as a terrorist organisation, with the aim of dismantling its military structures in the Gaza Strip and excluding it from political power.
It remains to be seen whether the Arab parties will agree to all demands.
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