The accomplished goalkeeper picked up a serious shoulder injury midway through this past campaign and was ruled out for the rest of the season.
However, Baxter has since disclosed that Khune is on the road to recovery and could have been ready to do duty at the continental showpiece.
“Khune worked hard. He was given a program that will have him ready to play by the start of the season,” Baxter told Isolezwe.
“He is working with the conditioning team to get ready for next season," the former Malmo FF and AIK shot-stopper continued.
Bafana are under the guidance of Lee's father, Stuart Baxter, who coached Khune at Chiefs during his three-year spell with the Naturena-based giants.
“Regarding joining Bafana Bafana for the Afcon, if it was up to me I would have him in the Afcon squad but I don’t have the power to make that kind of a decision," he concluded.
Bidvest Wits shot-stopper Darren Keet, SuperSport United vice-captain Ronwen Williams and Chiefs starlet Bruce Bvuma are the keepers, who have been included in the Bafana squad.
Keet is most likely to serve as South Africa's first-choice keeper at the Afcon finals which will be hosted by Egypt between June 21 and July 19.
South Africa have been drawn into Group D at the Africa Cup of Nations, which kicks off on June 21 in Egypt.