In Rodgers' first season in charge last term, Liverpool finished seventh in the Barclays Premier League and so far this summer they have added to their squad by bringing in goalkeeper Simon Mignolet, defender Kolo Toure and forwards Luis Alberto and Iago Aspas.
Asked about his relationship with Rodgers, Gerrard - also the England skipper - said: "I think it's perfect.
"I've got a lot of respect for Brendan as a coach, but also as a guy as well.
"I've loved every minute of working with him since he came through the door and I hope he is here for certainly the next couple of years. I want to work with him more.
"The relationship is growing and I feel as if he is the man to take this club forward."