According to the Mirror, Chelsea and Manchester City are tracking the youngster, who is yet to agree terms on a new Liverpool contract. The two title contenders are believed to be monitoring Sterling's contract talks with Liverpool, and the Anfield club have now stepped up their efforts to reach an agreement as they look to try and ward off interest.
Rodgers is keen to sort out a package before the New Year, when the transfer window opens and the likes of City and Chelsea can make offers for the 18-year-old winger.
The Mirror reports Liverpool have since stepped up their efforts to tie Sterling down to a new long-term deal, and extensive negotiations are now taking place.
But the report also suggests Arsenal are monitoring Sterling's ongoing contract wrangle, and could be tempted to make a move if the price is right.
The teenager, who turned 18 last week, made his England debut under Roy Hodgson in the 4-2 defeat to Sweden last month.
Since making his Liverpool debut last season, the young winger has enjoyed a rapid rise to stardom, and has flourished under Reds manager Brendan Rodgers.
But until he agrees terms on a new deal, he still has 18 months left to run on his current contract, clubs like Chelsea and City will circle, and may look to tempt Sterling away from Anfield.