WASHINGTON—The federal regulator who oversees Fannie Mae and Freddie Mac is pushing to speed up the mortgage giants’ exit from 12 years of government control but has yet to reach an agreement he needs with Treasury Secretary Steven Mnuchin, according to people familiar with the matter.

Mark Calabria, a libertarian economist who heads the Federal Housing Finance Agency, has made it a priority to return Fannie and Freddie to private hands, a goal shared by Mr.