Both North (dead leg) and Scarlets team-mate Williams (facial injuries) were helped off during the 27-19 first Test defeat in Brisbane and have been receiving intensive treatment since.
However caretaker coach Rob Howley is confident the duo will now be able to train fully in the next session and be available to him for the weekend.
"Both players trained light on Tuesday morning and we are hoping they will both be able to train fully on Thursday," said Howley. "We have a day off on Wednesday as it is a travel day.
"Touch wood they will both be available for selection for Saturday."
Howley was forced to send on his Brisbane try-scorer, Alex Cuthbert, when Aled Brew injured his hip in Tuesday's 25-15 win over Brumbies, a fixture largely populated by the fringe players.
Cuthbert was himself taken off as a precaution in the second half when he went down in a heavy tackle. Another injury worry would have been a real headache to the Welsh coaches.
"We were cautions sending Alex on," admitted Howley. "He's obviously gone down and it is nothing untoward really and I think he will be fine for selection for the weekend."
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The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
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