The Reds acted quickly in the transfer window to bring in four players already, but their manager insists they are still busy identifying potential new signings
The Reds have already brought in Luis Alberto, Iago Aspas, Simon Mignolet and Kolo Toure since the transfer window opened, but missed out to Borussia Dortmund on rumoured target Henrikh Mkhitaryan.
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"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."
The Reds begin their pre-season campaign with a friendly against Preston North End on Saturday, and Rodgers is looking forward to getting a look at his new signings in action.
"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."