Baxter and former Orlando Pirates mentor Ruud Krol have both recently been linked with the post after SAFA's negotiations with Carlos Queiroz, Herve Renard and Hugo Broos fell through.
SAFA plan to name Shakes Mashaba's successor before interim coach Owen da Gama oversees Bafana's friendly matches against Guinea Bissau and Angola on March 25 and 28.
"Look, I've got Supersport directors here tonight and I'm sure they'll be asking me that question as well," Baxter told reporters after his side beat Royal Eagles 2-1 in the Nedbank Cup last-32 last night.
"Every conversation I had with my directors is, I'm SuperSport coach and I don't know anything more than that.
"I hear all the talk, speculation, I hear that. And from what I know and from what I understand, there are some moves being made and what those moves entail I genuinely don't know. I honestly don't know.
"I'm not at that sort of meeting with the officials of SAFA. I know there's conversations and I want to keep myself away from that until someone tells me 'listen, SAFA have made an approach to us and this is what it is', and when I know what it is I can then give my opinion of it.
"But until then it seems a bit weird for me fueling more speculation, so I'll leave it with the club.
"I could tell you for an hour about national football and the attractions of it and the lack of attractions of it, but until we know exactly the position then it'll be strange of me and maybe a little bit stupid of me to comment," concluded the Brit, who coached Bafana from May 2004 to November 2005.