Former Bafana Bafana coach Carlos Queiroz and two-time Afcon champion, Herve Renard were previously linked with the job.
However Safa's found it difficult to break Queiroz's contract with Iran, and also then would have to keep up with his high wage demands on top of that.
The 'bomb' landed in the media when SuperSport United announced that they will give Safa permission to speak to their British coach, Baxter on Thursday.
"SuperSport United has given permission to The South African Football Association (SAFA) to engage their Head Coach Stuart Baxter with a view to him becoming the Head Coach of Bafana Bafana," read the statement.
One of the problems is that the potential appointment would only allow Baxter to start on 1 July 2017.
On United's Instagram post there's already a number of interesting responses from fans, even though we must remember that Baxter might not be the only candidate remaining.
@supersport_unitedfc has given permission to The South African Football Association (SAFA) to engage their Head Coach Stuart Baxter with a view to him becoming the Head Coach of Bafana Bafana. If negotiations between SAFA and Mr Baxter are successful, and SuperSport United and SAFA agree on an early termination of Mr. Baxter's current contract, such appointment would only be effective at the end of the current PSL season, officially commencing 1 July 2017.
This is what our editor Ignat Manjoo had to say about the latest development.
"I've already written in the past that Baxter would make a good choice, and that I preferred Queiroz and Renard.
"The more I think about it, Baxter's appointment won't excite me. It's not just about bringing back a coach who failed in the past, because I believe coaches can improve in time and can deserve a second chance, in which case the former Kaizer Chiefs coach has proven he's progressed," writes Manjoo.
"Rather, the problem is that I don't believe there's a significant difference in quality between Baxter and Gavin Hunt or Pitso Mosimane (or even Gordon Igesund). So, I'd rather select a local coach any day of the week than a foreigner at the same level.
"It's not compulsory to select a foreigner in any case. And, if we do (why?) then Baxter has advantages over Ruud Krol and Renard, in that he's worked in the PSL in recent seasons, winning honours and will know our players and culture very well.
"For those reasons I'd be relatively happy with the appointment. When you look at Safa's great ambition for this role, judging from their comments in the media, I can understand that the fans are now going to be underwhelmed," Manjoo concluded.
Well, this is exactly how the public responded:
In 2004, Baxter replaced Mashaba as a Bafana coach. Bra Shakes must be thinking: "not you again". — Zola Doda (@ZolaDoda) March 30, 2017
If Stuart Baxter & Safa talks are successful for Bafana Bafana coaching job then the Scotsman can take over after 2016-17 season on 1 July.. — Mathews_mpete (@MathewsMpete) March 30, 2017
I hope Stuart Baxter declines that Bafana job. I would rather have Gavin Hunt take the job instead. This thing of recycling same faces— kamo (@Kxamo_) March 30, 2017
Shakes Mashaba to Stuart Baxter, recycling at it's best. Jomo Sono & Carlos Queiroz are next then Clive Barker will try get us to Qatar 2022 — Gastro (@Gastro_o) March 30, 2017