Dayan, formerly head of the Yesha Council, lives in Ma'ale Shomron in the West Bank .
Rousseff's disapproval places Prime Minister Benjamin Netanyahu, who also serves as foreign minister, in a dilemma, as Dayan's appointment was approved by the government two weeks ago.
According to diplomatic protocol, when a government appoints an ambassador, it sends his or her name to the host government and asks for its permission (in diplomatic jargon, an "agrément").
A host government's refusal to accept an ambassador is very rare, and usually, in order to avoid a diplomatic incident, it is customary to transmit hushed messages conveying that it would be better to retract the candidate's appointment so as not to encounter rejection.
Dayan and settlers would likely be angered if Netanyahu retracted the appointment If he stands by his nomination and in the end receives an official refusal, this could cause a crisis in Israel's relations with Brazil. Netanyahu sees relations with Brazil as an important strategic goal for Israel. Brazil is the largest country in South America, with a population of 200 million, and it has the seventh largest economy in the world. Israel has made a point of developing trade relations with the international markets in Latin America, particularly with Brazil.
Netanyahu's associates have not lost hope and believe they will eventually persuade Rousseff to approve the appointment, arguing that Dayan represents the government of Israel and its policies.
As reported recently in Yedioth Ahronoth, 40 well-known organizations in Brazil have signed a petition calling on Rousseff to decline approving the appointment on the grounds that Dayan's appointment is a violation of international legitimacy and a challenge to the sovereignty of Brazil. Several Brazilian MPs have also joined the protest.
Netanyahu announced Dayan's appointment on August 5, and the government approved the appointment on September 6.
Politically, relations with Brazil have improved over. On Thursday they abstained from voting at the General Conference of the International Atomic Energy Agency in Vienna on the proposal to impose supervision on Israel's nuclear facilities. This is considered a change in Brazil's voting pattern, which used to automatically vote against Israel.
Dani Dayan, 59, was born in Argentina, and has an MBA in finance. He was chairman of the Yesha Council between 2007-2013 and was called the the settlers' "foreign minister" due to his notable public relations skills. Dani lives in the settlement of Ma'ale Shomron settlement, about 10 kilometers east of Qalqilya.
One possibilite outcome is for Netanyahu to retract Dayan's appointment and appoint him ambassador to another country.
On Sunday, the government is expected to approve Netanyahu's request to appoint Zvi Heifetz ambassador to Moscow. A few months ago the government approved the appointment of Heifetz as ambassador to China replacing Matan Vilnai. For an unknown reason, Netanyahu changed his mind and decided to leave Vilnai in China and send Heifetz to Moscow.
Despite repeated requests, the Prime Minister's Office refused to comment on the report. The Foreign Ministry also declined to comment. Dani Dayan said: "I suggest you contact the Foreign Ministry. I do not know about that."