The 18-year-old winger became an England international this season after a series of eye-catching performance for Brendan Rodgers' side. But a contract wrangle on Merseyside has left the door open for Arsenal and Manchester United.
The Sun report claims the Premier League pair are set to battle it out for the £15m capture of Sterling. The teenage winger has just 18 months left to run on his Liverpool contract, and is believed to want a bumper pay-increase after his meteoric rise to Liverpool and England stardom.
The pressure is now on Liverpool to sort out a deal for Sterling, with Arsenal and Manchester United breathing down their necks.
But The Sun reports that contract talks between Sterling's representatives and Liverpool have stalled, opening the door for the likes of Manchester United and Arsenal.
Arsene Wenger and Sir Alex Ferguson could be set to compete then, when the January transfer window opens next month. Both clubs are expected to be busy in the window, with Arsenal in particular linked with a number of targets.
But the signing of Sterling would definitely send shockwaves across the Premier League. The youngster is regarded as one of England's brightest prospects, and has come on leaps and bounds since making his Anfield debut last season.
Sterling made his England bow last month in the 4-2 defeat to Sweden, and the young playmaker would become the first player to transfer between Liverpool and Manchester United since Phil Chisnall almost 50 years ago if a deal between the two parties is agreed.