Rodgers says the Reds have spoken to a number of rival clubs about unnamed players and he remains hopeful of agreeing deals in the next fortnight.
Liverpool have signed two players - Swansea midfielder Joe Allen and Roma forward Fabio Borini - since Rodgers replaced Kenny Dalglish in May.
But the Northern Irishman insists he will not be rushed into buying players who do not fit his vision for the club's revival.
"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."
Under Dalglish, the Reds finished a disappointing eighth place in the Premier League last season - their worst league position for 18 years.
Rodgers has allowed Dirk Kuyt, Craig Bellamy and Fabio Aurelio to leave Anfield, but has resisted a major overhaul of the first-team squad he has inherited.
He added: "We obviously haven't brought in too many players, but there are some players that have gone out for a number of reasons.
"There is still a lot of work to do within the group and there will probably be more changes between now and the end of August in terms of ins and outs.
"Come the end of August when everyone is here, we can be real focused and be together, and start on the journey to hopefully having a real good campaign."