This is according to a report by local publication Sport24, who claims to have been reliably informed of Baxter's future.
Baxter's second spell hasn't been too rosey with Bafana having failed to qualify for the 2018 Fifa World Cup finals, while they have also failed to win the Cosafa Cup on two ocassions despite being the hosts.
When Baxter took over from Owen Da Gama, who had replaced Shakes Mashaba on an interim basis, Bafana were strong favourites to win their group and qualify for the Fifa World Cupfinals.
However, back-to-back losses to Senegal as well as their dismal performance against Cape Verde saw them fail to qualify for their second successive World Cup finals.
The former Amakhosi mentor has been in charge of 17 matches for Bafana, and while he has beaten one of Africa's powerhouses in Nigeria, he remains under pressure for the time being.
Bafana face Nigeria on November 17 at the FNB Stadium before travelling to Libya for their final Group E match in March next year.
They remain second on the log despite their draw away to Seychelles not so long ago, but they have to win at least one of their remaining two matches to book their plan ticket to Cameroon.
According to the publication, Gavin Hunt has already been earmarked as Baxter's possible replacement.
Both Baxter and Benni McCarthy are also linked with Hunt's job at Bidvest Wits.