The Reds manager is content that Arsenal's interest will not come to fruition after the in-demand striker attended his side's 1-0 Premier League victory over Stoke City.
Arsenal has pursued the Uruguayan for much of the summer but has not upped its bid from its most recent, which was said to be more than 40 million pounds, and the Reds boss was adamant on Friday that the saga would not "sabotage" his club's season.
The forward was in attendance as Liverpool opened the Premier League campaign with a 1-0 victory over Stoke City, and Rodgers seemed content that there would be no more question of an exit.
"The only thing I will say about Luis is that I am very satisfied how everything has been resolved and now we can move on," Rodgers told reporters. "He is a part of this team and this club. The supporters are a class act here, and it is the classic Liverpool way to support the players and the manager."
Suarez is unavailable for the next five games as he continues to serve a 10-match ban incurred last season for biting Chelsea's Branislav Ivanovic.