Sterling has yet to put pen-to-paper on a contract extension at Anfield - despite the fact he was offered a £100,000-a-week deal earlier this season - and has been linked with both Chelsea and Real Madrid in recent months.
Marsh feels Sterling will leave Liverpool in the near future, regardless of whether or not he signs a new deal with the Reds.
Marsh: Sterling will join a big club
“They are talking about his new contract and all these numbers but I think Raheem Sterling will definitely not be a Liverpool player in the not too distant future,” he told the Sports Bar on talkSPORT.
“He may stay another year or two but, ultimately, he will be at a big football club.”
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Sterling on course to become world star
Sterling has been a revelation at Anfield since making his debut for the Reds in 2012, and came agonisingly close to becoming a Premier League champion last season as Brendan Rodgers' side finished second in the table.
The 20-year-old went on to impress for England during the Three Lions' brief World Cup appearance in Brazil and picked up the coveted Golden Boy award in December.
It's scary to think how good the young winger could become if he continues progressing at his current rate.
Bilic: Sterling can become Premier League's best
Earlier this month Besiktas manager - and former Everton defender - Slaven Bilic tipped Sterling to become the Premier League's best player in an interview with The Sun.
“He can be the next big player in English football. The best,” Bilic stated. “He’s got the speed and the confidence.
“He’s not the strongest but he’s everything but afraid. He goes into tackles and is very strong. Most definitely he can be. He’s not yet but he can be and he should be."
Although Sterling's current contract does not expire until June 2017, Liverpool are acutely aware that failure to tie him down to a new long-term deal before the summer leaves them more vulnerable to losing the player.
Jamie Carragher blasts agent
It seems his representatives are a problem for the Merseyside outfit. Back in October, Liverpool hero Jamie Carragher took to Twitter and blasted the youngster's agent for "feeding stories" to the media about his contract situation.
Liverpool should be worried
No agreement between Sterling's agent and Liverpool has been reached, almost five months later, and there must be concerns amongst the Reds' faithful that the bright lights of the Bernabeu or Stamford Bridge will eventually lure the lightning-quick winger away from Anfield.
Marsh is wrong to hint Liverpool are not a big club - although it's true that Real Madrid, the world's biggest club, are in a different league.
Liverpool fans: are you worried that Raheem Sterling will leave Anfield in the near future? Which could could he join next? Have your say in the comments below!