The former forward has offered a warning to the Liverpool youngster, citing the failure of former Manchester City star Sean Wright Phillips as an example of how things can go wrong.
The young forward is yet to sign a new contract at Anfield despite months of talks, with it being revealed last night that he is set to ask for a move away from Anfield, according to the BBC.
He has so far been linked with a potential move to a number of big clubs, but Heskey has warned him against such a switch, citing the example of Wright-Phillips as evidence of how things can go wrong.
“He should also be mindful of what has happened to other bright talents in the past, like Shaun Wright-Phillips,” he wrote.
“Shaun was England’s hottest prospect at Manchester City but then he moved to Chelsea where he was not playing anywhere near as regularly. In the end Shaun stagnated and went from the hottest prospect to someone who struggled to get a game.”
Heskey, though, insists that the club must do all they can to keep hold of the England man.
The ball is very much in Liverpool’s court when it comes to a transfer, with there still two years left to run on his current deal, leaving them in a similar situation to that of the Luis Suarez saga from two years ago.
And while he is likely to leave for a big fee should he move clubs, Heskey says it would likely be difficult to replace him unless they have someone else lined up already.
“If I were in charge at Liverpool, I would sill be doing all I could to keep him,” he added.
“They would need to go out and pay big money to bring someone else in. Big clubs only let big players leave when they have someone lined up, and I don’t think Liverpool have as yet.”