Meredith missed training this Thursday after twisting his ankle earlier in the week. The Australian will be assessed in the build up to the match at the Pirelli Stadium, with Greg Leigh likely to deputise in his place if needed.
Kyel Reid is back in training after an injection in his knee at the start of the week, whilst Reece Burke is making progress after a recent Achilles injury.
Lee Evans serves the final game of a three-match ban at the weekend but Jamie Proctor is back available for Parkinson after being ineligible for last Saturday's victory over Fleetwood Town.
Parkinson said: "Mezza (James Meredith) twisted his ankle slightly on Tuesday.
"That was obviously a blow for us but we have a very good deputy in Greg Leigh if James can't make it for Saturday.
"Reidy had his injection on Monday. He had a few days rest to let that settle down and now he is back in full training again. Reece Burke doesn't look like he'll be too far away as well."
With work still on-going to improve the club's training facilities at Apperley Bridge following the recent wet weather, Parkinson's men trained at West Riding County FA headquarters in the Woodlesford, Leeds on Thursday.
Filipe Morais took part in the warm-up with the rest of his team-mates as the Portuguese winger continues his recovery from the serious knee injury he picked up in pre-season training last July.
Parkinson added: "It is good to have him (Filipe Morais) back involved for training.
"He did the warm-up with the lads and then took part in some specialist individual drills with Nick (Allamby, Head of Sports Performance).
"He is at that period when he's been with Matt (Barrass, Head Physio) for quite a few months now and the specialist is really pleased with his knee.
"We can now slowly start filtering him back into training and getting him doing some specific work to help his recovery.
"He is a great character to get back out on the training pitch and we're pleased to see him out there.
"I'd like to thank the West Riding County FA for letting us use their facility today (Thursday).
"It is almost like a little hidden gem tucked away in this part of Leeds - it is a fantastic pitch."