Celtic manager Ronny Deila insists Virgil van Dijk does not want to leave the Scottish Premiership leaders in January.
Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
The 18-year-old England international has broken into the first-team picture to great effect at Anfield this season and has so far made 25 appearances for Brendan Rodgers' men.
He made his England debut against Sweden last month and with his contract on Merseyside running down, talk was rife that he could move to one of a number of potential suitors.
That has been put to bed, though, with Sterling opting to remain with the Reds.
Despite the security of a long-term deal, Sterling vowed to continue learning.
"There's a lot more to be done," he told the club's website. "I haven't begun yet as the manager has said it's just been good to get a few minutes on the pitch and hopefully I can kick on after the New Year and try to do my best for the team and the football club."
Sterling moved to Liverpool from QPR in February 2010 and made his debut as a substitute against Wigan in March.
The arrival of Rodgers proved to be the catalyst for a more consistent run in the team, with his England debut then making him Liverpool's youngest-ever international.
On Rodgers, Sterling added: "I can't say much more about the guy than what has already been said - he's a brilliant manager.
"The way he speaks to both young and senior players, you have to really compliment him for that. He just treats every one as one and that's really good to have at a football club.
"In the New Year, you can expect more from Liverpool, especially when the manager gets his players in. We'll stride forward and hopefully do what we know we can do."
In the immediate future for Sterling and Liverpool is a Barclays Premier League clash against Fulham at Anfield this evening.
The Cottagers have won just twice in their last 11 league matches on the road - although one of those was their first victory at Anfield last May.
No Fulham player has scored in their last six visits to Anfield - Reds defender Martin Skrtel scored an own goal last season - but after last week's chastening 3-1 defeat to Aston Villa Rodgers is taking nothing for granted.
"They have some terrific players, Martin Jol is very experienced and a good manager, (Dimitar) Berbatov is on the top of his game at the moment," he said.
"They are a team which has been strong at home in the last few years in the Premier League but away from home they've found it difficult.
"Our concentration has to be on ourselves because if we worry too much about the opponent then what might happen is what happened last weekend.
"It is about getting our own mentality right and if we do that we will continue to climb the table.
"My concern is just to keep moving forward and keep our performance level at a good level."