The Northern Irishman has signed Fabio Borini and Joe Allen already during the transfer window, but suggested further players could be joining them.
"We hope that within the next number of weeks those will bear fruit" Rodgers told the club's official website.
"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.
"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."
The former Swansea manager also stated that he is impressed with his current crop of players.
"The players are developing very well and I've been extremely pleased with the attitude and the application of the group since I came in," he explained.
"It's been difficult because a lot of the players returned at different times, but we've played two competitive games already and I've been encouraged and enthused by what I've seen.
"There's no doubt that we always have to be looking to evolve and get better, and that's something myself and the club are looking to do with the team.
"But certainly at this stage we're in a good moment and we're really looking forward to the first game - and we'll look to get started with a nice positive result."