The 23-year-old German, who joined the Reds from Mainz in the summer, has been sidelined since late July after breaking a bone in his hand in a pre-season match against Chelsea in the USA.
Karius underwent an operation this week and will soon begin training in a bid to return to action at some point in the coming weeks but says he will not putting any pressure on setting a date for his comeback.
"I had surgery on Wednesday, so now the wires have been removed that they put in four weeks ago," he told Liverpoolfc.com.
"Now the fracture has healed, hopefully I can start training now and build it up.
"I don't know if it is going to be a week or however long [before I am back in full training], I just need to see how it feels. But I can now start using my hands and catch balls. It's up to me now, basically.
"We're ahead of schedule because in total it's been about five weeks [since the injury] I think, but I don't want to rush it too much. Now I am in the last stages, I just want to feel good and confident about it, that it's all done.
"I am not going to rush it because of two or three days, but if I feel good then maybe I will be back way sooner than expected."