Parkinson has added full-back Danny Imray and central midfielder Ben Whiteman to his ranks ahead of the trip to the Riverside Stadium.
Imray – who signed a four-year deal with Wrexham after leaving Crystal Palace – made his debut in the 1-0 pre-season loss to Sunderland on Sunday.
Midfielder Whiteman officially completed his move to north Wales from Preston North End on Tuesday night.
“I’m very pleased, two really good players,” Parkinson said of his newest recruits.
“Danny came out on the tour with us which was good for him.
“Ben’s just joined us this week, it’s been a bit of a crazy week for him to join because he hasn’t seen much of the lads, but he was training fully today.
“He’s a really experienced Championship player, he’s got great leadership qualities and I’m looking forward to working with him and Danny.”
Parkinson remains eager to further bolster his options before the 23:00 BST transfer deadline on Tuesday, 1 September.
And the experienced manager – who has guided Wrexham to three promotions since taking charge of the club in 2021 – believes his side still have plenty of work to do in the market.
“We feel we’re not where we need to be yet and we know that,” he added.
“We’re working, as ever, to make sure that the squad is as strong as it needs to be in what is going to be an incredibly competitive division.
“We’re under no illusions about that. We’ve got to make this squad so strong and we are working tirelessly to bring those extra players in to give everybody a boost.”