Meredith, who scored in City's home match against Sheff Utd last season, missed Tuesday's draw with Southend United after jarring his right ankle during last Saturday's encounter at Oxford United.
McCall says Meredith is feeling better and they will leave it as late as possible before making a final decision over the left back's fitness.
The City chief said: "He (James Meredith) is improving all the time, he is recovering well.
"We'll look at him in more depth tomorrow (Friday).
"He's had another session with the physios today and he feels very positive.
"He is, of course, desperate to be involved as well.
"He certainly has a better chance of playing this Saturday than he did last Tuesday.
"He is one that we will have to probably make a late decision on."
With Marc McNulty deemed ineligible to feature against his parent club, City will be forced into at least one change to their side from the eleven that began against Southend on Tuesday.
Thinking ahead to the game and his team selection, McCall admitted he could be open to making more than just the one alteration to his side though.
Taking into consideration Meredith's pre-match doubt, Tony McMahon, who expected to return to training on Monday, is the only senior player definitely unavailable to McCall this weekend due to injury.
He added: "We have players who are desperate to be involved again. Equally though, there are players who have just come into the side and who want to keep their shirt.
"I don't like to tinker too much if things are going well but I do like to pick the side depending on what I feel is best for an individual match.
"Looking at Tuesday night as an example, I felt it was best for Rory (McArdle) to come back in to compete against a 6' 3'' physical striker in Nile Ranger.
"There is always the chance to go back to Romain (Vincelot) at centre half though.
"We will look at all areas of the pitch."