The Foxes are the only Premier League club yet to sign a new player during the transfer window so far, with much of the focus being on offloading fringe players in order to free up funds and squad space.
However, moving players on has been easier said than done so far, with the only departures being backup goalkeeper Eldin Jakupovic, following the expiration of his contract, and Ademola Lookman, who has returned to parent club RB Leipzig following the end of his loan spell.
With many Leicester supporters being frustrated at the absence of incomings this summer, Rodgers has remained calm and refused to criticise the club as things stand.
Speaking after their 3-3 draw with Leuven in a pre-season friendly on Saturday, Rodgers said: "I trust the club implicitly. It's a club that has always given me everything they have had since I've been here.
"Clearly, we have to do some business out before we can get players in. We just are not in the same position as some of the other clubs.
"Until that changes, I keep working with the players we have. We try to maximise their abilities and if the club can do something in the market to help the team, we would want that.
"(Selling players) is two-way. Other clubs have to want the players. But it's also very important that we can't get too hung up on that.
"Of course I want to improve the squad, I want to develop the squad, I said that midway through last year, but if it's difficult financially, I really respect the club, so I won't go to war with them.
"It's unfortunate. We have to do some work and if we can do that, then hopefully we can affect the squad because if we are going to compete anywhere near where we have been, then we need to be able to do that. If not, then it's a different expectation."
With just three weeks to go until the start of the Premier League season, Rodgers has admitted that he will not have been able to strengthen his squad as much as he would have liked during the transfer window.
Rodgers added: "Hopefully we can improve the squad, but my honest opinion is that it's not going to be the level I would have wanted. But that's just unfortunate.
"It was also off the field as well. We wanted to reset some of our work off the field and we have started in that process, which is great, but of course I want the strongest squad possible. But if that's not possible, then I will work with the players I have and we'll continue to fight and work the very best we can."
Whilst an expected move for Youri Tielemans to Arsenal has failed to materialise so far this summer, Leicester have been keen to offload the likes of Jannik Vestergaard and Hamza Choudhury.
The Foxes are also open to selling Caglar Soyuncu and Ayoze Perez, who like Tielemans, have entered the final 12 months of their contract at the King Power Stadium.