Sterling, 20, joined the Reds from QPR back in 2010, and has become one of Liverpool's star players over the last 18 months.
The Jamaican-born forward hit ten goals in 38 games last season, and has now racked up ten goals in 35 games this term, starring under Brendan Rodgers.
However, his exploits have led Sterling to demand a new contract - despite only signing a new five-year contract in December 2012, which took him on to £30,000-per-week, according to the BBC.
It's being reported that Sterling has rejected a contract worth £100,000-per-week, and is looking to earn even more money from the Reds.
Sterling has subsequently been linked with a move to Premier League rivals Manchester City, but former Reds hero John Barnes has words of warning for Sterling.
He told talkSPORT that Sterling should look at Aston Villa winger Scott Sinclair and Sunderland midfielder Jack Rodwell as examples of how careers can stall with a move to Manchester City - or another club - too soon.
"Raheem Sterling should absolutely sign the contract and stay at Liverpool," said Barnes. "I would advise any young player who has just been in the game for a year or so to stay and learn his trade. Show a level of consistently over a four or five year period before you make a big move. You will then be judged as a £50m player."
"We’ve seen it with Scott Sinclair and Jack Rodwell at Manchester City. Where are they now?" he added, noting that neither player made an impact at the Etihad Stadium during their time with the club.