The Northern Irishman also made a bid for Willian before the Brazilian signed for Chelsea, and the former Swansea City boss has said that they are still looking at options before the September 2 deadline.
"We're still trying to do some business before the window closes," Rodgers told reporters.
"We're hoping to come out of the back of the window with a stronger group of players. The ones we've got are doing brilliantly and I've every faith in them being a success if we don't add to the squad.
"The idea for us is to strengthen the squad that little bit more [before the deadline]."
Liverpool have won both of their Premier League games so far this season.