Rodgers's side are currently sitting in seventh place in the Premier League, just nine points behind Tottenham Hotspur in fourth.
With the Merseyside club's form improving, having lost just one of their past six league games, Rodgers believes that a Champions League spot is still in sight.
"We've got nine points difference [to Tottenham], and we can do it, there's no question about that," said the former Swansea coach.
"We've had a lot of tough games, and we've got a lot of big rivals for those places to come at home. As I've said, our form at home is getting better, we're scoring goals, we've been defensively strong, the crowd have been magnificent, so we sense a real opportunity.
"It's a lot of points to make up, but we're certainly going to fight. We're certainly going to accept the challenge that's in front of us and I believe that the players, if we continue to play how we have been and retain that focus and mentality, then we'll have a terrific chance."
Liverpool face West Bromwich Albion on Monday night.