The Merseyside outfit finished seventh last season, but nine games into the new campaign, the Reds are two points adrift of the top spot in the table, which is currently occupied by Arsenal.
While Rodgers has described the club as being in a "good moment", the Northern Irishman is not getting carried away with Liverpool's chances of title glory.
"We want to be up there challenging and winning trophies, that's what Liverpool is all about," Rodgers said in a press conference. "We won't get carried away.
"I believe we are in a good moment. We have started the season as we would have wanted and I think we can only get better and improve."
Liverpool could go to the top of the table if they overcome the Gunners in this Saturday's clash at the Emirates.