The teams will meet in Bloemfontein on Friday.
Nyakane had been left out of the Springbok squad for breaching team protocol and would not feature in the Rugby Championship over the next couple of weeks.
The Cheetahs' scrums lacked power last weekend against the Western Province in Cape Town and, with prop John-Roy Jenkinson struggling with an ankle injury, Drotske was positive Nyakane would fill the void at scrum time.
"From our perspective it is good to have Trevor back," Drotske said.
"We struggled in the scrums last week and we need him because we are a little bit thin on the ground after losing Coenie Oosthuizen and Adriaan Strauss to the Springboks."
Drotske said Nyakane could bolster the Cheetahs, not only at tight head, but also on the loose head side if needs be.
"Trevor can play loose head and tight head," he said.
"His versatility is what makes him such a valuable player. Not many guys have the same ability to play on both sides of the scrum."
Rossouw de Klerk was brought in as a replacement on the bench after looking impressive in his First Division game for the Griffons last weekend.
"If Caylib Oosthuizen does get injured, Trevor can shift back to loose head and Rossouw can fill the gap in the number three jersey," Drotske said.
In other changes to the side, lock Lood de Jager would replace the injured Waltie Vermeulen, with Teboho Mohoje coming into the starting line up.
Freddie Ngoza had been included as lock cover on the replacement bench.
Sarel Pretorius would again start at scrumhalf with Kevin Luiters coming onto the bench in the place of Piet van Zyl, who had been called up to the Springboks.
"Prop is the one position where we are not lacking any depth," Drotske said.
"Lock now seems to be the problem, but Francois Uys will hopefully be ready next week and Waltie will also be back.
"Then the picture looks a bit better."
Cheetahs team: Hennie Daniller, Riaan Smit, Johann Sadie, Robert Ebersohn, Raymond Rhule, Elgar Watts, Sarel Pretorius, Philip van der Walt, Lappies Labuschagne, Boom Prinsloo (captain), Lood de Jager, Teboho Mohoje, Trevor Nyakane, Hercu Liebenberg, Caylib Oosthuizen. Replacements: Ethienne Reynecke, Rossouw de Klerk, Freddie Ngoza, Davon Raubenheimer, Kevin Luiters, Willie du Plessis, Joubert Engelbrecht. – Sapa