The Foxes find themselves firmly among the teams that are vying for top spot in the Premier League.
After narrowly missing out on Champions League football last term, Rodgers would love them to go even better this time around.
Leicester take on Chelsea in a huge top of the table clash on Tuesday.
"We are in the race, we are competing and we are consistently up there," said Rodgers to reporters.
"We are enjoying the race and enjoying the challenge.
"There's maybe not the same expectation at Leicester as Liverpool and Celtic, which are huge institutions. But what I've tried to do from day one is deliver a message for us to feel that pressure to perform.
"We know our budget is different to what a so-called top-six club's would be but I want us to feel that pressure to keep pushing and developing. That will never lessen in me.
"The people and fans at Leicester are realistic but the club showed it when they won the title in 2015-16 that everything is possible, and that sense of realism should never stop us dreaming.
"I've always liked being around the top echelons of the league and if you come in each day trying to be better, you never know where it can take you. I've always tried to sell that message to my payers.
"We are happy in the race and hopefully this year we'll show we can keep going and improving."