The manager says he has heard "nothing whatsoever" regarding an extension to his deal, which expires in 2015.
Liverpool is fourth in the Premier League after 25 matches this season, six points behind leader Chelsea, as it continues to improve under the Northern Irishman's tenure.
Rodgers has 17 months left on his current deal and so far he has heard nothing from the club's owners regarding a potential prolonged spell in charge.
"If I never get offered one I would give my life to the last day of that contract. In the meantime, until anyone says otherwise or wants to reward the staff or myself for our work, then we keep working as normal and see where it takes us.
"The option is for the club for the fourth year, but in all fairness there is a point next year where the club has to let me know whether they want to keep me on or not.
"I have regular contact with the owners and it is never mentioned. I talk more about players. My ambition is more for the club so I want the players tied up so we can keep the best players here and get players in.
"The club knows my feelings in that I love it here and I've started out on something I would want to hopefully — if I can progress and be good and everyone is happy — stay here and continue. If it's not to be for the owners and they want a different direction at the end of it, I will have done my best."
Rodgers also highlighted the progress of Jordan Henderson, who has become a key part of Liverpool's midfield after initially struggling, and reiterated he could be in line for a new contract of his own in due course.
"The way he is working, we would want to secure his services," Rodgers added. "He still has all his best years ahead of him and you can see his growth and development. He will want to get better and I'm sure it is in the interests of the club to tie him down. Jordan, tactically, is improving so much, and [Steven Gerrard] is in the zone just behind."