The Anfield boss saw his side get their Premier League campaign up and running on Saturday with a 1-0 victory over Stoke City.
Striker Suarez was in attendance as a Daniel Sturridge goal gave the club their first opening-day win since 2008 - despite being banned for the encounter as he serves the remainder of his 10-match suspension for biting Chelsea defender Branislav Ivanovic.
"The concentration is on the players who are available to play," Rodgers said. "Luis is doing his work, there is nothing to be said there.
"I'm very satisfied with how everything has been resolved, as a club we are looking to the future and moving on."
The Ulsterman dismissed claims that the Brazilian's Anfield arrival was imminent, but confirmed his intention to add numbers before the deadline.
He said: "We're confident of having one or two in before the window shuts. (Willian rumours) are just speculation really."
