The new Reds boss has signed Fabio Borini and Joe Allen since arriving at Anfield from Swansea City but has revealed that he wants more quality to strengthen his squad by the close of the transfer window.
"There has been contact and communication with the clubs," Rodgers told the club's official website.
"The team of people behind myself are working very, very hard in relation to those targets.
"We hope that within the next number of weeks those will bear fruit.
"The work has been continual right the way through to try and get in players that fit the profile of Liverpool and the team. I would hope there would be a couple more signings before the end of August."