Coleman picked up a knee injury in a Premier League clash against Leicester City back in May and there were initial fears of a lengthy time on the sidelines for the defender.
"It was a significant injury but I am recovering well, hitting all the targets so far, being back on the grass over the last few weeks, not with the team but with the physios, back with the ball," the 34-year-old told Irish publication The 42.
"Slowly but surely, it's starting to feel better. Without putting a target on it, because that's not what they are doing as such, it's about reaching points and scores in the gym before you can move on.
"At the minute, I am doing all of that. In six to eight weeks, maybe, I will be back at it fully and feeling good."
The captain could be back in time for the Merseyside derby at Anfield on Saturday, 21 October, but he is unlikely to feature in the Republic of Ireland's Euro 2024 qualifiers against Greece and Gibraltar.