The Merseyside club have overcome their worst ever start to a season, losing only one of their last six fixtures in the top flight, and currently lie 10th in the table.
Liverpool captain Steven Gerrard believes qualification for the Champions League is possible but Rodgers hopes they do not limit their ambitions to sneaking into the top four.
When asked if a fourth-place finish was possible, Rodgers told reporters: "So is third, so is second and maybe even first. I said to the players this morning that everyone talks about fourth place but what about third?
"We are 11 points off second so, if we can get some consistency, keep our mentality and our focus then it is not fourth place we want to aim for. We have still to play Manchester City and we should have beaten them at home.
"You want to aim as high as you possibly can but, of course, when the club has been out of the top four for so long, that is the ultimate ambition. But we will not get too carried away. We are not even halfway through the league.
"We just need to focus day-to-day on our work, tactically prepare the team, keep confidence high and keep as many players available as we can in order to get results."
Rodgers took over from Kenny Dalglish at Anfield in June and expressed his delight at the application of his players in implementing his distinct ethos of possession-based play.
"I am always positive with the players because I've seen their work, their honesty and I see their willingness to take responsibility," he enthused.
"I want to reinforce that it isn't just about fourth place for this club. This club is bigger than that. OK, we might not arrive there this season but everyone is talking about arriving in fourth position when there is not that big a difference between us and third.
"There is not that big a difference to second. There are 17 points between us and Manchester United and that is a big ask, of course, but 11 points isn't and four points certainly isn't. There is real belief in the group. They believe in what we are doing."