The 33-year-old has been out of action since the opening day of the season when he suffered ligament damage in his thumb.
However, the experienced shot-stopper is now expected to be back in contention during the middle of October.
"He is training with us now and doing well," Taylor told the club's official website. "He is pushing on, which is good, and he will be delighted to be back out there.
"He is not ready for first-team football yet but I don't think that is going to be far away. I would say a couple of weeks max."
The Gills are currently in 12th place in the League One table after taking 12 points from their first nine games of the season.