Giteau, who went under the knife last month, had his first run with the Wallabies at their training camp in Coffs Harbour on Tuesday, and looked to be moving well.
However, Cordingley re-injured his foot during the same session and his position on the reserves bench for this Sunday's Test against England in Sydney is in doubt.
"He's a bit sore, and we'll know more in a day or two," Australia coach John Connolly said about Cordingley in the Sydney Morning Herald.
"It is something we'll have to keep an eye on."
Cordingley was the standout Australian scrum-half in the early rounds of the Super 14 this year with the Queensland Reds but his season was cut short when he damaged ligaments in his foot just six weeks into the competition.
Connolly had been looking to rotate Wallabies captain George Gregan and Cordingley behind the scrum for the upcoming internationals with the Reds number nine expected to be named in the starting line-up for the second Test against England or the match against Ireland on June 24.
If Cordingley is forced out, his Queensland back-up Josh Valentine is expected to be named on the bench this weekend.
However, Giteau's situation was more encouraging, although there is still a question mark over when he will be available for selection.
"It was pleasing seeing Matt running for the first time today, but I'm not sure when he will be coming back," Connolly said.
"It could be the second Test against England, or the Ireland Test. Really there's no point rushing him."