Maj Gen Halevi currently serves as deputy to outgoing Chief of General Staff Lt Gen Aviv Kohavi.
The nomination is to be discussed by an advisory committee in the coming days before the government gives its approval, Mr Gantz's office said on Sunday.
Maj Gen Halevi is due to take up his new position in February next year, the Defence Ministry told AFP, after Lt Gen Kohavi's term ends.
Mr Gantz called Maj Gen Halevi "the most suitable officer" for the position owing to his "extensive operational experience in a variety of theatres of operation" and his "commanding abilities and attitude to various military issues".
Prime Minister Yair Lapid welcomed the decision to nominate Maj Gen Halevi, whom he called "a worthy and natural choice".
"I am certain that he will lead the IDF [Israeli Defence Force] to many significant achievements," Mr Lapid said.
Born in Jerusalem in 1967 to a religious family, Maj Gen Halevi was enlisted in 1985 as a paratrooper and advanced in various command positions before joining the elite Sayeret Matkal commando unit in 1993, the Israeli army's website said.
He served as commander of the unit for three years from 2001 and then continued to climb the ranks, becoming head of military intelligence in 2014 and head of the southern command in 2018, the army said.
Maj Gen Halevi has degrees in philosophy and business management from the Hebrew University and a master's degree in resource management from National Defence University in Washington, the army website said.
Maj Gen Halevi is married with four children and lives in Kfar Haoranim, a community that is partially a settlement in the occupied West Bank.