Sterling has rejected a £100,000-a-week deal and has delayed discussions on a new deal until the end of the season.
Arsenal, Manchester United, City, Chelsea, Real Madrid and Bayern Munich have all been linked with the 20-year-old.
Sterling insists he wants to win trophies and on the prospect of winning the FA Cup this season, he said: "It would be extra special for me because it is my home town."
PA
Raheem Sterling has been urged to stay at Liverpool next season
Meanwhile, Daniel Sturridge believes lifting the FA Cup could usher in a new era of success for Liverpool.
The England striker insists a win at Wembley can provide a "platform" for the club to go on and win silverware on a consistent basis.
Liverpool face Aston Villa in the semi-final a week on Sunday and while Sturridge is taking nothing for granted he cannot help but dream of the season ending with a silver lining.
Daniel Sturridge Injury Record
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"It would be huge for everyone, the fans, the players, the manager," said Sturridge.
"We have waited a while to have some success and hopefully it can be this season.
"It could be a platform for a long-standing timeframe of success."
