Baxter has been in contact with Untersee since his return as senior national team coach in May last year, with the hopes of convincing him to play for his country of birth.
The 24-year-old right-back, who is currently on loan at Serie B side Empoli from Juventus, was born in Roodepoort on the West Rand of Johannesburg.
He moved to Switzerland at a young age and represented the Swiss junior national teams from Under-15 through to U-21 level until 2014.
However, Baxter on Tuesday morning confirmed that Untersee has since committed to turning out for Bafana ahead of The Nati.
Untersee has been on the books of The Old Lady since October 2010, when he joined their U-17 team from FC Zurich juniors, but has yet to make a first team appearance, spending most of his time out on loan.
He has made 13 appearance for Empoli this season – managing four assists, but has fallen out of favour in recent times, making just one sub appearance since the end of November.