Having lost the first Test 27-19 in Brisbane, Wales must win on Saturday to keep the three-match series alive.
Both North (dead leg) and his Scarlets team-mate Williams (facial injuries) were helped off the field in the opener and have been receiving intensive treatment for their ailments.
Caretaker coach Rob Howley is confident they 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. We have a day off on Wednesday as it is a travel day," said Howley.
"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 midweek 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. He's obviously gone down and it is nothing untoward really and I think he will be fine for selection for the weekend," admitted a relieved Howley.