Rodgers has been speaking to the media ahead of a pre-season friendly with a Malaysia XI this week.
Christian Benteke is reportedly set to become the seventh signing of the summer when his move from Aston Villa is completed, as covered by the Daily Mirror, but Rodgers remains coy when it comes to discussing any further arrivals, with the Reds' transfer business now expected to turn towards offloading those deemed surplus to requirements.
The Reds' boss told reporters, including those from the Liverpool Echo, at a press conference in Malaysia: "I've got a real inherent belief that the players we've brought in can help us push on this season.
"We're really hopeful that we can push on and challenge on all fronts.
"I'm only interested in talking about players that I currently have here. Not about players coming in, or going out.
"I'm very happy with the players we've brought in. We had to bring in quality and ambition."
So far the Reds have won all three of their pre-season games. as new signings start to integrate themselves into the squad, with Roberto Firmino the only fresh face yet to link up with his new teammates following his participation with the Brazil national side at the Copa America.
It was a disappointing season for the Reds last term, failing to win a trophy and finishing sixth place - very underwhelming considering the previous season saw Liverpool come within two points of winning the Premier League title in the most extraordinary circumstances.
There is a lot of pressure on the manager and the side to perform well this season, and that means they need to get off to a good start. They have two more pre-season friendlies against a Malaysia XI and HJK Helsinki remaining, while a second string side may be put out against Swindon Town before the start of the season.
Rodgers will want a 100% record from pre-season in order to generate some momentum for his side going into a tricky-looking start to the campaign.