The Amakhosi coaching job remains vacant two months after Steve Komphela resigned as the club's head coach towards the end of the 2017/18 campaign.
Chiefs have been linked with several foreign coaches such as Israeli mentor Avram Grant, French tactician Patrice Carteron and Egyptian coach Hossam El Badry, but they ended up losing their targets to other clubs.
Carteron was recently appointed head coach of Egyptian giants Al Ahly and El Badry joined Egypt's Al Ahram FC, while Grant has been linked with Greek giants Panathinaikos.
Former Chiefs mentor Baxter has since emerged as a target for the Soweto giants, who are looking to appoint a new coach, before the 2018/19 season starts this August.
"Well, Baxter is a good coach and I do not think Safa will allow him to go back to Chiefs," Mayo told Goal.
Baxter was appointed Bafana Bafana head coach on a five-year deal last year and the South African Football Association (Safa) are keen to hold on to the British tactician.
"The coach is still contracted to Safa on a long-term deal and I think they still want him to continue building a strong national team," the 45-year-old continued.
"But if it happens that Chiefs reach an agreement with Safa which would see him return to them, then it would a great thing for the club," Mayo added.
Baxter, 64, enjoyed a lot of success while in charge of Chiefs - winning two PSL titles plus the MTN8 Cup and Nedbank Cup between 2012 and 2015.
"For me he is the right man to lead the club at the moment and he has what it takes to revive a big team like Chiefs," the retired defender-come-striker explained.
Komphela endured three frustrating seasons under Komphela between 2015 and 2018 - failing to win major trophies.
"He knows exactly what is needed at Chiefs and he understands the culture of the club," Mayo said.
"He was very successful in first spell with the club. So, I believe that Baxter would hit the ground running if he does return to Chiefs," he concluded.