German international Hamann, whose expert defensive protection has been sorely missed by captain Sami Hyypia, could soon join Kirkland in training and should be ready for first-team action in November.
Gerard Houllier has warmly welcomed the quick recuperation of two players integral to his Anfield plans for the current campaign.
It's good news Chris has returned to training. He needs to build up his fitness now and needs games," said Houllier.
"Didi should be able to start running either next week or the week after. He needs to get his fitness back and then match fitness with some reserve games.
"When Didi saw a specialist at the start of the season he said he would be out for three months, so he is doing well and I would say he should be back in November."