The 38-year-old English striker is showing he has not lost any of his quality, as he scored a goal in injury time during a 4-1 win over Celtic on Sunday.
Defoe has six goals from 18 games this term, and Gerrard would prefer that he sticks around for another season.
The ex-Tottenham man has been linked with a return to Sunderland.
"He's been a wonderful player. He's had a wonderful career. To get him up here in the first place was something I was keen to do, because I knew he would help the group in the way he goes about his business. He's a top professional.
"We're in talks with Jermain at the moment about what's next for Jermain. But we want to be really respectful, we want to give him the time to make his own decisions.
"I think he's at a stage in his life where we'll listen to Jermain and see what he wants to do moving forward.
"We'll go from there. I don't think it's right for me to divulge right now what's been said from my point of view and from his. But we'll certainly respect Jermain in terms of his own decisions moving forward."