The Reds sealed a £20m deal for the ex-Southampton stalwart earlier this summer, and Lovren claims that Rodgers has spotted some leadership qualities in him akin to those of Carragher.
"The manager said he sees me like a leader. I said to him I'm still young. I'm 25, but I will try my best. I will lead the team," Lovren told The Guardian.
"I don't have so much experience like Jamie Carragher but it will come and it is a great honour to be compared by the manager with a player like that.
"I like to talk during the game, I like communication with the lads – to keep me awake apart from anything else. But it's the beginning."
The 25-year-old could face the Saints on his Liverpool debut at Anfield on Sunday.