Eriksson, who has been unemployed since leaving Leicester City last year, warned the 32-year-old that he must act as quickly as possible if he is to lift the Premier League trophy before the end of his career.
"Steven Gerrard is Mr Liverpool and has won the Champions League, Super Cup, FA Cup and League Cup with them," said Eriksson.
"But the question is whether he will ever win a Premier League title. As things look now, absolutely not.
"A lot of things have to change at Liverpool for that to happen.
"The owners have to pump in money and buy the right players. Andy Carroll and Stewart Downing have been such expensive signings, but they've not been a success in the red shirt.
"When I look at their team today I see just three world-class players: Pepe Reina, Gerrard and Luis Suarez.
"Without them a Champions League place is very far away. I don't begrudge a good guy like Steven winning the league. But maybe he needs to change clubs if he wants to have that title."
Eriksson added that his advice for Gerrard is not born out of animosity towards the Anfield club.
"Both my dad and I have been Liverpool fans since the club’s heyday in the 1980s," he said, "but the Liverpool we see today are far from the top level."