Rodgers has already captured Luis Alberto, Iago Aspas, Simon Mignolet and Kolo Toure, and he believes those acquisitions have sufficiently improved his squad.
Now the Northern Irishman is focused on bringing in players who will boost his first-choice XI.
"Our recruitment team are doing a great job behind the scenes in compiling lists of players that we can afford and might be available for us," Rodgers, who failed to provide an update on unsettled striker Luis Suarez, told the club's official website.
"What we've done in the early part of the summer is to improve the squad. That's something I feel we've done with the players we've brought in.
"Now what's important over the next three to five weeks is improving the team. That's something the club is working very hard at.
"I'm sure by the time the end of August comes we'll be ready and we'll have a terrific squad ready to challenge."
Liverpool get their pre-season underway on Saturday at Preston North End and Rodgers says all four new signings will feature.
"There's every chance. All of the players are working here," he said. "If they are all well and fit then they will travel for the game on Saturday.
"Simon Mignolet will play, of course; Aspas, Luis Alberto and Kolo Toure -
they will all get a run-out."
Toure, one of Rodgers' summer signings, hopes he can play a major part in helping the club regain its Champions League status.
"It has been a tough time but this season is going to be a great season for Liverpool, he said.
"To be part of the team who can bring the club back to the Champions League would be amazing. That's what I'm looking for.
"I would like to be remembered as someone who did very well and that is why I am here.
"At the moment Liverpool are not in the top four but they have the history, the quality, the players and the mentality as well.
"This club is a winning club and I want to be part of history here, that's why I came - to try to build the team as far as we can, to be top four or to win a trophy.
"We just want to win trophies and want to play in the Champions League as well.
"There are a lot of good teams out there but with the squad we've got, we have great players and a great mentality here, we can do very well this season."
Fellow new signing Simon Mignolet is also confident the club can make the top four again.
His first task may be to displace Jose Reina as first-choice goalkeeper but he knows the bigger picture is to regain Champions League status.
"For me it's a big step forward. I spoke to the manager and he told me that it's going to be a big step forward," said the former Sunderland goalkeeper.
"There's big ambition around the club. I also noticed that from the conversations I had with the goalkeeping coach and the gaffer.
"I saw that they are very ambitious, want to get forward, winning trophies and getting into the top four."