The 32-year-old midfielder said that he understands he will need to change how he normally plays under Rodgers's philosophy, and insists that he will develop his game.
"Yes, I do, because he's got a different philosophy and way of playing to other managers I've worked for," Gerrard told the BBC.
"There are certainly things I can still improve on by working with him. I'm enjoying working with him on a daily basis, and I think my form recently has been really good.
"I'm enjoying my football, and I'm really looking forward to the next two years I'm contracted for and hopefully more, to add some chapters to a career I'm really proud of."
Liverpool host Stoke City at Anfield in the Premier League on Sunday.