Taylor, who scored a stunning 30-yard strike in the Carling Cup triumph over Sheffield Wednesday, sustained the injury last Friday afternoon and was subsequently forced out of the 2-2 draw at Hereford over the weekend.
But his rehabilitation is going to plan and the 25-year-old is likely to line up against the Mariners, although boss Micky Adams is refusing to confirm his availability just yet.
Adams told the club's official website: "We were very disappointed to lose Kris at such a late stage last week as he is someone who had been doing well for us.
"That said, I felt Damien McCrory came in and took his chance well and I was happy with his contribution.
"Kris has been responding well and we are hopeful he will be available for the weekend. It's a little early to say at the moment so we will have to see how we get on later this week."