An official in Netanyahu's office told AFP the Israeli premier was "very likely" to attend Bolsonaro's inauguration ceremony in January.
Bolsonaro on Thursday announced his intention to relocate the Brazilian Embassy from Tel Aviv to Jerusalem once he formally assumes the presidency. In a tweet published on Thursday, Bolsonaro said: "Israel is a sovereign state, and we shall duly respect that".
Brazil would become the second major country after the United States to do so.
Judge Sergio Moro, who led Brazil's massive anti-corruption drive, just pulled into the driveway of the house of Jair Bolsonaro, Brazil's right-wing president-elect, for a job interview.
Jair Messias Bolsonaro, Brazil's new president-elect, said he plans to visit Israel soon and move Brazil's embassy in the country from Tel Aviv to Jerusalem, following the courageous lead of the US.
Bolsonaro, a controversial hardliner who has earned the nickname "Trump of the Tropics", won Brazil's presidential election last month with roughly 55 percent of the vote, ending a 15-year era of the far-left Workers Party.
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But for opponents, the move fuelled accusations that the judge was politically motivated - especially against leftist ex-president Luiz Inacio Lula da Silva who, according to opinion polls, would have beaten Mr Bolsonaro in the election had he not been jailed for 12 years for corruption.
The move will make Brazil the third country, behind the US and Guatemala, to move their embassies.
Bolsonaro has often expressed admiration for Donald Trump and appears poised to follow the US president in a radical overhaul of his nation's foreign policy.
Despite the vote, the United States went ahead with the embassy transfer on May 14, triggering demonstrations in the occupied Palestinian territories, Iran, Turkey, Egypt, Jordan, Tunisia, Algeria, Iraq, Morocco and other Muslim countries.
In December, President Donald Trump reversed longstanding USA policy and recognized Jerusalem as the capital of Israel, prompting Palestinian president Mahmud Abbas to boycott his administration.
The Palestinians claim east Jerusalem, which was captured by Israel in the 1967 Mideast war, as the capital of a future state.
John Bolton, Trump's national security adviser, said Mr Bolsonaro and the Trump were "like-minded" individuals.