Yehuda Glick, a member of Prime Minister Benjamin Netanyahu's right-wing Likud party, will meet Heinz-Christian Strache "next week in Vienna", the spokesman said.
Glick is also due to meet Austrian Foreign Minister Karin Kneissl, another senior figure in Strache's far-right Freedom Party (FPOe), the spokesman said without further details.
The FPOe agreed a deal with Austria's conservatives in December to set up a coalition government following elections in October.
The Israeli government said at the time it would work with the new Austrian coalition government but "for the moment" would not have direct contact with FPOe ministers.
Netanyahu said he planned to have direct contact with the country's chancellor Sebastian Kurz, head of the Christian Democratic party.
Public radio quoted sources close to Glick saying the planned meeting had been given the green light by Israeli authorities.
Founded by former Nazis, the FPOe emerged in the late 1990s as the main far-right force in Europe.
Israel suspended relations with Austria when the FPOe entered the government in 2000, eventually normalising them in 2003.
Strache, 48, has sought to soften the party's image and has visited Israel several times, the last time in April 2016 when he met members of Netanyahu's government.
He has been an outspoken criticism of Islam in Europe, calling for a partial ban.
The left wing Israeli party Meretz condemned the planned meeting, saying the "hate of Muslims pushed the Likud to whitewash antisemities".