The News of the World says Hodgson will get until the end of the season to prove to the new owners he's the right man to lead a Liverpool revival.
Despite the club's poor start, Hodgson's job is under no immediate threat following the Kop takeover by New England Sports Ventures (NESV).
But Hodgson will be told to deliver a blueprint to his new bosses detailing how he intends to rebuild the ailing squad.
NESV will expect Hodgson to show the vision and inspiration required to prove he has a long-term role at Anfield.
A Kop source said: "The new owners will be fully supportive of Roy and give him time to succeed.
"It's incredible how quickly people have forgotten Roy inherited a squad in decline which finished seventh last season and lost in the FA Cup at home to Reading. Roy has come in and had no quality left back, no full-back cover for Glen Johnson and only one established striker.
"On top of that he's had to deal with all the problems regarding Javier Mascherano wishing to leave and others being unhappy because of the lack of Champions League football.
"Everyone knows the team has to improve immediately, but there is no way Roy's job is already on the line.
"He'll get the same support previous managers received when they took the job. They didn't exactly hit the ground running in the league."