The 34-year-old midfielder is contracted to the Reds until May, having been with the club since he was nine years old.
And while Gerrard has expressed a desire to remain at Anfield, Manchester City boss Manuel Pellegrini has not ruled out a move for the ex-England skipper, who has scored scored three goals in 13 Premier League and Champions League games this season.
"It is certainly not sentimental [to offer new terms to Gerrard]," Rodgers told several national newspapers.
"As the manager of this club you can't afford to do that. Look at his contribution in the two years that I've been here.
"Steven was 32, had struggled with injury, hadn't played consistently over a number of years, and I came in, sold him the idea and the philosophy of how we wanted to work and his importance to it.
"In that period, he has been absolutely outstanding and of course maybe the team hasn't played so well this year, and maybe there's a focus on Steven, but he's been absolutely brilliant for me.
"Both on and off the field, as a leader and a captain I want to ensure that on this second curve we're on, in terms of the development of this group, he is very much a part of that.
"So there is certainly no sentiment involved in it. When you see his influence in the changing room, he is still an outstanding player.
"He will be 35 at the end of the season but he is still fresh and he still looks after himself very well. Technically he is a big player for us. He is the perfect sort of example for a lot of our players to learn from."