Socialist Prime Minister Pedro Sanchez, who came to power in June, had vowed to remove Franco's remains from an imposing basilica in the Valle de los Caidos (Valley of the Fallen) near Madrid, which was built in part by political prisoners during his regime.
Spain's cabinet meets on Friday and will give its final green light to the exhumation of Franco, said a government source, who refused to be named.
The family will be able to appeal this at the Supreme Court, which would delay the exhumation.
The source said the government would also give the family two weeks "to decide on a place for the (re) burial and, if they don't do it, the government will decide."
The bid to exhume the remains of Franco, who ruled from 1939 to 1975, has run into difficulties.
Franco's family wants to bury his remains in a crypt at Madrid's central Almudena Cathedral next to the royal palace.
The government wants Franco's embalmed body to be relocated to a more discreet spot and has already told them this will not be possible.
Sanchez is currently in a tough situation with Catalan separatist lawmakers in the national parliament ready to block his 2019 draft budget this week, a move that could lead to snap elections.