The Reds defeated Olympiakos earlier today in the US.
"I'm really pleased with how it's all coming along," said Rodgers. "Our World Cup players have just come back.
"We have only just been together as a squad over the last week or so. I know the group well and I know those coming in will fit what we're trying to do. When the Southampton game (at Anfield on August 17) comes up, we will be ready for that."
Of the performance against Olympiakos, Rodgers added: "I was delighted with the team. As pre-season goes well, we will be getting sharper in our movements and passing but, at this time, we are building up the resistance of players and getting minutes under the belt.
"In the first half, our passing was crisp and precise. We looked real threat at top end of the field. I was also very pleased with how we defended. We are in good shape and I am delighted."
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