Former England manager Sven-Goran Eriksson suggested that the 32-year-old is running out of time and should leave the Merseyside club.
However Rodgers, who joined Liverpool from Swansea this summer, thinks that Gerrard is in the right place to achieve his goals.
"I think Steven, over the years, has had a number of chances to leave here," said Rodgers.
"He has always felt that this is the club where he could still win it and he has still got a number of years left in his career.
"Of course we will go through difficult moments - but his dream is to win the Premier League with Liverpool."
The Liverpool manager also paid tribute to the way Gerrard has served the club over the years.
He continued: "He is an iconic figure for this football club. His status and everything he has gained in the game has come through Liverpool.
"He has won every major honour you could possibly win with this club but obviously there is one missing and he will fight for the rest of his career to win it here."
Liverpool are preparing for the Europa League qualifier against Hearts tomorrow night.
Rodgers rested the likes of Gerrard and Luis Suarez for the first leg in Scotland, but the pair could feature at Anfield.