Israel's president will name Netanyahu as candidate for the premiership, with the incumbent having already shored up rightwing and centre-right support guaranteeing him the parliamentary majority he needs for a fourth term in office.
Netanyahu's victory in polls last week has exacerbated a diplomatic crisis with the United States, bringing frosty ties between him and President Barack Obama into focus and exposing differences over the moribund Middle East peace process.
"We'll know tonight who has been charged with forming a government," a spokesman for Rivlin told AFP.
"The president certainly feels that... We need stability, and we need it quickly," he said, adding that Rivlin would "press upon the candidate the importance of getting it done as soon as possible."
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Netanyahu surged to a surprise victory in last week's general election, beating the rival centre-left Zionist Union by 30 seats to 24 in the 120-member Knesset (parliament).
But Israel's political system requires the government to have a parliamentary majority, meaning in reality that every prime minister has to form a coalition cabinet.
Following two days of consultations, Rivlin is due to formally name Netanyahu -- but only after he is presented with the official election results Wednesday evening.
Netanyahu will have four weeks to complete the task of forming a new cabinet, although Rivlin can extend the deadline by another 14 days if necessary.
There will then follow weeks of coalition horsetrading as Netanyahu's potential partners battle for portfolios and prestige.
Moshe Kahlon, head of the centre-right Kulanu party and a former Likud member, has reportedly already been offered the finance ministry.
"Netanyahu decided not to wait and began to put the puzzle together, starting (Monday)," an editorial in Maariv newspaper wrote.
"The prime minister met with... Kahlon and as he said he would do... He promised him the finance ministry.