The Foxes, who have started the campaign with a draw and a loss, have only signed back-up goalkeeper Alex Smithies so far amid a difficult summer at the club.
Any signings are largely dependent on players being sold, with Chelsea having had two bids rejected for Wesley Fofana and Newcastle also being denied in an attempt to sign James Maddison.
Rodgers is beginning his fourth full season in charge at the King Power and, having recently delivered back-to-back top-five finishes in the Premier League, expectations may have to be tempered.
“Let’s see where we’re at in a few weeks when we’re into early September,” he said ahead of Saturday’s visit of Southampton..
“For me, we’ll wait to see where we are when the window ends. What I do know is that I’ve got a group of players that are so keen to learn.
“I love working with them. It’s the longest I’ve ever been at a club, which tells you how much I love working with the players here and being involved with the football club.
“My ambition is to always improve and develop and that’s what we’ll look to do again this year.
“If we don’t have these resources to improve and develop, then we have to try to find other ways to be able to do that. The people I feel for at the minute for the supporters.
“We’ll always look to progress and move forwards and maybe we don’t have the financial clout to be able to do anything thus, I would never sit in my seat.
“In my life, I’ve never been a manager who likes to stand still. I’m no good at just maintaining, I need to be building and creating.
“In order to be the best of myself and to give that to the club, for me, I will always be looking to progress myself and the team.
“Whether we have finances or not.
“With a few weeks to go, you never know, something might drop for us and then we can push on. Either way, if it doesn’t, we’ll be doing everything we possibly can, every single day, from early morning to late at night, to keep developing and be as competitive as we can be.”
Rodgers is boosted by news of Harvey Barnes’ return from injury for the Saints clash.
Barnes has missed the start of the campaign due to a knee problem but has returned to training this week.
“It’s great news for us,” Rodgers said. “Harvey Barnes is back in training so that’s really good for us.
“He’s looked excellent, he’s looked fit. He had a really good pre-season so it was a blow to lose him for the opening two games.
“He should be available, but we’ll decide whether he’s going to be in from the start. He’s looked good in training. He may be available to start, but it might not be 90 minutes. We’ll assess that in our final session.”