The Sun says Gerrard, 32, has just a year left on his current contract and the new offer will see a likely rise in his £130,000-a-week wages.
Gerro said: "The talks have started but I think it is something that will get sorted at the end of the season.
"It's not a stand-off or anything like that. They want me to extend, I want to extend. How long for I'm not too sure yet. That's under discussion."