Johnson has been blamed for failing to impose his will on the England squad during the tournament, which his team exited at the quarter-final stage following defeat to France.
The BBC reported that Johnson and England’s director of elite rugby Rob Andrew would hold a press conference later today.
Johnson, 41, who lifted the World Cup with England as captain in Australia 2003, has been the team’s manager for three-and-a-half years.
England’s tournament in New Zealand was blighted by images of senior player Mike Tindall apparently drunk in a Queenstown nightclub after a group stage match, and “inappropriate” remarks made by players to a female member of hotel staff in Dunedin.
Tindall was fined and dropped from the England squad for his conduct relating to the drunken night out.
But Johnson defended Tindall, who was forced to apologise for misleading the England management about his movements that night.
The off-field antics continued to hit the headlines even after England were knocked out of the tournament, as Manu Tuilagi was detained by police and fined by his England bosses for leaping off a ferry into Auckland harbour.
Following the World Cup, Chris Ashton, one of the players to have joined Tindall on his night out, made a veiled criticism of Johnson’s performance as manager.
“We played this whole tournament in a different way from the way we played in the Six Nations and I don’t really know why we did that,” Ashton said. “The way we played at the start of the Six Nations is the best way for us to maximise the talent we have in the squad, without a doubt. But we didn’t do that. We didn’t use what we’ve got and I don’t see any point in that at all.”