Mr Herzog was set to meet teams from both sides on Tuesday evening at his office in Jerusalem, the presidency said.
Prime Minister Benjamin Netanyahu will not be in attendance, Israeli media reported, as he is banned from intervening in judicial reforms due to his ongoing corruption trial.
The PM announced a pause in judicial legislation on Monday after a nationwide strike had brought the country to a standstill.
Foreign ministry employees, doctors and thousands of others joined protesters across Israel demonstrating against the proposed reforms introduced by Israel's most right-wing government yet.
Airport traffic to and from the country's biggest airport, Ben Gurion, was also halted.
The protests intensified after Mr Netanyahu fired defence minister Yoav Gallant for criticising the legislation. Right-wing government ministers responded to protesters by joining counter demonstrations in Jerusalem.
Mr Netanyahu said he was pausing further readings of the bill until after Passover to avoid "a rift in the nation".
The government has been pushing for changes that would limit the Supreme Court's powers to rule against the legislature and the executive, while giving coalition politicians more power in appointing judges.
The panel for selecting judges requires sitting politicians and judges to agree on appointments. The present proposal would change that, giving the government decisive sway.
Israeli activists and Palestinian citizens voiced alarm over the new government after a right-wing and ultra-religious alliance helped Mr Netanyahu reclaim power following the November elections.
The cabinet, the most right-wing in Israel's history, has already taken steps to expand Israeli settlements in the occupied West Bank and expand administrative power in Palestinian areas.
It comes amid heightened violence in the West Bank, where daily army raids have already killed more than 20 Palestinians so far this year.