North midfielder Jaidyn Stephenson remains a chance to feature for the side this weekend against Richmond despite being subbed out with a hip complaint in the latter stages of the Roos' close encounter with Collingwood last weekend.
"Jaidyn has progressed really well, especially in the past 24 hours. He'll be on a modified session at main training tomorrow and we hope he'll be available this weekend," White said.
"He received a knee impact into his lower back and hip area early in the third quarter and as the game progressed he was struggling with running function and change of direction.
"We obviously removed him from the game due to that lack of function, but he's recovering well at the moment."
"Kayne has recovered well from his head knock and progressed through modified football loading over the weekend," White said.
"As long as he gets through main training on Wednesday he'll be cleared and available for selection."
Veteran rebounding defender Aaron Hall is getting closer to a return after suffering a quad strain in the opening minutes of the Kangaroos' clash against the Cats in Round 16.
A week after breaking the AFL record for metres gained, Hall pulled up sore in the early stages against Geelong after dashing out of defence and was subsequently subbed out of the game.
White said a return next week would be likely for Hall should he tick off the necessary checkpoints in his recovery.
"'Hally' is progressing well with that minor quad strain. The plan this week is to build his speed, acceleration and footy function in a gradual manner away from the main group," he said.
"This will have him better placed to return next week and enhance his ability to finish off the year strongly, rather than rush him to be cleared this week."
Young key forward Charlie Comben is set to increase his efforts towards an end-of-season return after recovering from a knee operation he underwent ahead of Round 12.
The 20-year-old was in strong form at VFL level for North and will be hoping to impress in the final rounds of the season.
"Charlie had surgery to remove screws from a previous operation that were causing him pain and limiting his high-end football function," White said.
"Post-recovering he's now graduated through Alter-G running loading and on-field running loading, and he's now transitioning back into football conditioning.
"We want to build his football loads over the next two weeks, and if he tolerates that block well we plan to have him available in Round 20."
In more positive news for North fans, midfield bull Ben Cunnington could also be set for a return to football in the coming weeks, with the veteran overcoming a calf injury.
"'Cunners' is progressing really well through his strength and running loading," White said.
"We'll look to reintegrate him into football training next week and build towards a return to play if he absorbs that loading phase well in the coming weeks."
However, the club have confirmed that they put experienced wingman Jared Polec on ice for the rest of the season, with the 29-year-old struggling in his recovery as he continues to experience pain in his surgically repaired ankle.
Polec hasn't played football since Round 3 for the club and, despite a return seeming close in recent times, they have announced that he will not suit up for the side for the rest of 2022.
"Unfortunately Jared is still at the point where he has pain in his ankle, and that's limited his ability to graduate to ground running and building solid conditioning on-field," White said.
"A conservative approach to enhance his recovery and maximise the status of the ankle will be the priority for the remainder of the season."
The club are hopeful, however, that luckless defender Kyron Hayden will get game time in the latter stage of the season, with the 23-year-old currently recovering from groin pain.
North Melbourne will face the Tigers on Saturday afternoon (4:35 pm AEST) at Marvel Stadium in what will be their first clash after David Noble parted ways with the club, with Leigh Adams to take the reigns for the rest of the season.