Springbok captain Jean de Villiers.
Springbok team doctor Craig Roberts said on Wednesday that both players had proved their fitness after responding favourably to treatment.
"Strauss has been running and he's ready to take part in a full training session," Roberts said.
"We'll see how he goes in Wednesday's afternoon session. "I'm happy with Jean's progress. He's been working out with Western Province and their staff informed me that he has recovered. He's ready to have a full training session now."
Strauss, the Bok vice-captain and hooker, injured his knee last weekend when he played for the Cheetahs against the Kings in the Currie Cup promotion/relegation play-offs.
Meanwhile, De Villiers suffered a hamstring strain during a training session with WP nearly two weeks ago. The other injury concern in the Bok camp is flanker Francois Louw, who injured his neck in an English Premiership game while playing for Bath over the weekend.
"I spoke with Flo [Louw] and his neck treatment has gone well, and it looks likely he'll be playing for Bath this weekend," said Roberts.
"He's suffered a pinched nerve some time ago and it may have flared up when he took a knock in a [recent] match.
"It's been a long, hard season and therefore the end-of-year tour is always going to be a challenge.
"At this stage of the year, the focus is to get the best of the players."
Bok coach Heyneke Meyer said the matter of injuries rested heavily on his mind and he felt the time had come to change the systems in place for the national team. The heavy workload of the Boks in recent months have resulted in numerous injuries and as a result, the side will tour without the likes of hooker Bismarck du Plessis, lock Andries Bekker, Pierre Spies, flyhalf Johan Goosen, Frans Steyn and wing Brian Habana.
Meyer felt South African rugby should take a leaf out of New Zealand's book and rest the players for extended periods in an effort to ensure good health. "Without wanting to be critical of the way things are done here, I would like to see changes in the systems going forward," Meyer said.
"I think New Zealand have got it right. They intend to rest [Richie] McCaw on their European tour.
"There are some great players with injuries when one looks at Frans [Steyn] and Bryan [Habana].
"Okay, JP [Pietersen] is back from injury, but the injured players can do a lot for the team, they are important for us.
"The [incoming] youngsters do well but when you have names like Habana and Steyn in your backline you have a really good team." – Sapa