Moore withdrew from the Wales squad during the international break because of a hamstring injury, but Parkinson says the forward is now making encouraging progress and will be assessed ahead of the trip to Suffolk.
"He is progressing. With Kieffer, he was frustrated to miss the internationals.
"The good news for Kieffer is that Wales have done well and got themselves in a strong position for the play-off games.
"They're both progressing well and we'll keep monitoring them on a daily basis."
Moore’s possible availability comes at a pivotal moment for Wrexham, who head into the weekend as one of the Championship’s form sides.
Since losing to Stoke in October, the Red Dragons are unbeaten in five league matches (W3 D2) and remain one of the division’s toughest teams to beat.
READ MORE: Give Me Moore! . . . Any Team in the Championship Would Love In-Form Wrexham Striker
Their opponents, Ipswich Town, have their own momentum.
The Tractor Boys are chasing a spot in the top six and have lost just one of their last 29 home league fixtures at Portman Road.
They have also been fuelled by the form of Jaden Philogene, the Championship’s top home scorer this season with six goals.
Saturday’s fixture marks the first-ever league clash between Ipswich and Wrexham.
Their only previous meeting came in the 1994-95 FA Cup third round, which Wrexham won 2-1 under Brian Flynn.
Parkinson himself has a strong record against Ipswich, having beaten them twice in 2020 during his time at Sunderland.
READ MORE: Phil Parkinson Hits Back at Critics As Wrexham Prove Their Championship Worth
Wrexham’s preparations, however, have been overshadowed by a significant injury setback.
Wing-back Issa Kabore will be out for at least six weeks after suffering a hamstring problem and is returning to parent club Manchester City for treatment.
"It looks like six weeks minimum. He'll do a lot of his rehab at Manchester City. He lives close to the training ground so that makes sense," Parkinson told BBC Sport Wales.
"He'll keep popping back to see us and we'll keep communicating with him.
"He's got the Africa Cup of Nations, but it looks like he's probably going to be touch and go for that."
Left wing-back Liberato Cacace is also recovering from injury, while Harry Ashfield has returned to action with the reserves.
READ MORE: Let’s Get it On . . . Wrexham and Cardiff City Both Keen to Crack on With Welsh Battle
Ollie Rathbone, meanwhile, has encountered another slight setback in his return to full fitness.
"Harry played for the reserves on Tuesday and did well. He scored a penalty," Parkinson said.
"Ollie, unfortunately, his thigh tightened up prior to the reserve game and we had to pull him out.
"He's just in one of those periods where you end up in a cycle of getting yourself to a certain position and something curtails him again.
"This is only a minor setback for him. He'll probably miss this weekend, but probably be close for the next two home games."
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