Meredith suffered some damage to his foot on Monday around the area where he suffered a fracture back in January. Despite some initial fears, however, it appears the left back didn't suffer any major damage to the area.
He was able to take part in full training today (Friday) and is now set for a substitute's appearance against the Dublin-based side at their Tolka Park ground.
Knott took a whack during Tuesday's UCD but he too was able to rejoin training at City's Irish base with the rest of the squad on Friday morning. The midfielder is expected to start the game.
Parkinson said: "With James (Meredith), I think the only real concern we had was because the discomfort was coming from the same part of foot he injured last season.
"He feels fine with it now though and he has trained fully today (Friday). He will also play some part against Shelbourne on Saturday.
"Billy just got a kick on Tuesday - it was nothing serious. He has been back in training today as well and he is now absolutely fine."
After beginning on the bench for Tuesday's match at UCD, the likes of Andrew Davies, James Hanson, Billy Clarke, Gary Liddle, Stephen Darby and Matthew Dolan are all in line to join Knott in City's starting eleven for the friendly on Saturday.
Aaron Mclean won't feature against Shelbourne though as he continues to recover from a calf problem.
Oliver McBurnie won't be involved either, while Lewis Clarkson, who has four goals in pre-season already, is expected to be rested as precaution due to a sore groin.
Parkinson added: "We will probably leave Lewis out for tomorrow (Saturday). He has worked really, really hard recently and we are pleased with his efforts but he has just got a bit of stiffness and soreness in his groin area.
"We are really pleased with his progress in pre-season so far but tomorrow is probably the right time to give him a bit of a break.
"We had hoped that Oli (McBurnie) might be in contention for this one (Shelbourne) but he still isn't back to regular training and it is something we will need to assess when we get back to England."