Bundesliga giants Bayern are the latest club to be linked with a move for Sterling as the 20-year-old England star continues to stall on a new contract.
But Hargreaves, who forged a glowing reputation during his seven-year spell in Munich by helping Bayern to four Bundesliga titles and a UEFA Champions League trophy, believes Sterling's development would be better served under Brendan Rodgers in Merseyside.
"I think he should stay at Liverpool for another four years," said Hargreaves.
"It will be good for his development.
"He is far too young mentally to make that move.
"Bayern are one of the best clubs in the world. Pep is a great manager. There is no better place in the world for a player like Sterling to be. He would fit in as good players always do.
"It would benefit him to play in such a team.
"But he should stay at Anfield a bit longer. Brendan Rodgers is also a great manager and will really develop him as a player."
