According to reports in the Sunday Mirror the Reds teenager is set to put pen to paper on a new £100,000-a-week contract to dash any hopes that Spanish giants Real Madrid might pounce.
Sterling still has three years left on his current deal but the plan at Anfield is to have a five-year agreement signed and sealed inside the next month.
Madrid have been monitoring the 19-year-old’s progress and were aware that his £30,000-a-week wages do not match his burgeoning reputation.
A Liverpool source said: “Talks with Raheem have progressed very well and we don’t see any problems arising from this point.
“There is no rush to get the contract signed, but we are now at a stage where we are talking weeks rather than months.”
The Spanish giants were ready to make a move next summer to link up Sterling with Cristiano Ronaldo, Gareth Bale and James Rodriguez.
The two sides clash in the Champions League later in the month.