The approvals are to include units in the flashpoint West Bank city of Hebron for the first time in years.
The official, speaking on condition of anonymity, said that "3 736 housing units will be approved at different stages of planning and construction".
He did not give a timeframe or a precise breakdown, but said the homes would be located throughout the West Bank, including in Hebron and at the Migron and Beit El settlements near Ramallah.
12 housing units
"In total, about 12 000 housing units will be approved in 2017, at various stages of planning and construction, four times the number in 2016," the official said.
Israel faced heavy criticism of settlement construction from US president Barack Obama's administration, but that has not been the case with his successor Donald Trump.
Israeli media say that a planning council is expected to meet next week to approve at least some of the plans.
Haaretz daily said that if the Hebron housing is approved it would be the first time for the southern West Bank city since 2002.
Hebron is home to around 200 000 Palestinians, with about 800 settlers living under Israeli army protection in several heavily fortified compounds in the heart of the city.
It is holy to both religions, with Old Testament figures including Abraham believed to be buried there.
The 1994 massacre of 29 Muslim worshippers in Hebron by Israeli-American Baruch Goldstein led to an agreement three years later giving the Palestinian Authority control over 80% of the city.
Israeli military rule
The settlers and about 30 000 Palestinians living adjacent to them fall under Israeli military rule.
Last month, Israel gave the settlers there the authority to manage their own municipal affairs in what critics denounced as reminiscent of "apartheid".
About 430 000 Israeli settlers live among 2.6 million Palestinians in the West Bank, occupied by Israel in the 1967 Six-Day War.
Settlement building in the occupied West Bank and annexed east Jerusalem is considered illegal under international law.
It is also seen as a major obstacle to peace as the settlements are built on land the Palestinians see as part of their future state.
Israeli Prime Minister Benjamin Netanyahu's right-wing coalition government leans heavily on settlers and their supporters to maintain its thin parliamentary majority.