Two signings are some way away from last summer's big-spending spree under Kenny Dalglish, but Rodgers has not given up hope of adding more new faces before the August 31 deadline.
Speaking to his club's official website, liverpoolfc.com, he said: "There has been contact and communication with the clubs. 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. Like I say, I would hope there would be a couple more signings before the end of August."