"The club are working very hard behind the scenes to manage that process to allow us to get some players in," Rodgers said. "But in terms of the depth, it is nowhere near where I would want it to be — we have a very small squad.
"I can't wave a magic wand to bring players in and get players out but there is still a bit of time left.
"Hopefully, come the end of August, we'll be ready to go on with the group we want."
Liverpool face Hearts in a Europa League qualifying match on Thursday evening.