The premier's Likud party said Netanyahu met Bennett on Friday, during which the former extended the offer. The appointment will be voted on at the next cabinet meeting, The Times of Israel reported.
New Right accepted the offer, said party official Ayelet Shaked, adding that Netanyahu had offered it a choice of two smaller ministries, from Agriculture, Diaspora Affairs and Welfare, or just Defence.
Bennett and Shaked famously gave Netanyahu an ultimatum in 2018, threatening to pull out of his government if the New Right party leader was not appointed Defence Minister, but ultimately backed down.
Bennett has relentlessly criticized the government's handling of violence from Hamas-run Gaza, demanding a harsher response, both when he served in the coalition and subsequently.
The current appointment is temporary.
Netanyahu currently heads a provisional caretaker government, after he failed twice to form a coalition following two general elections held on April 9 and September 17, respectively.
The mandate to form a government has passed to Benny Gantz, head of the centre-left Blue and White party which gained 33 seats in the second elections.
If Gantz fails to form a unity government together with the Likud, elections may soon be held in Israel for the third time.
The Blue and White party on Friday slammed the move as a "cynical ploy" by Netanyahu to hang on to power.
"Netanyahu continues to mortgage every position and every consideration to his bid for immunity," tweeted senior Blue and White MK Ofer Shelah, referring to Netanyahu's efforts to avoid indictment in three corruption cases.
( With inputs from IANS )